Very broadly speaking, you will want to train these in order. But of course, there are some qualifications to that:
Sources and Further References:
EVE University Short Skill Plan
EVE University Pyramid Skill Plan
EVE University The Magic 14
EVE University Support Skills
Alpha Friendly (up to at least Level III)
CPU Management 1
CPU Management 2
CPU Management 3
Power Grid Management 1
Power Grid Management 2
Power Grid Management 3
Capacitor Management 1
Capacitor Management 2
Capacitor Management 3
Capacitor Systems Operation 1
Capacitor Systems Operation 2
Capacitor Systems Operation 3
Mechanics 1
Mechanics 2
Mechanics 3
Hull Upgrades 1
Hull Upgrades 2
Hull Upgrades 3
Shield Management 1
Shield Management 2
Shield Management 3
Shield Operation 1
Shield Operation 2
Shield Operation 3
Long Range Targeting 1
Long Range Targeting 2
Long Range Targeting 3
Signature Analysis 1
Signature Analysis 2
Signature Analysis 3
Navigation 1
Navigation 2
Navigation 3
Evasive Maneuvering 1
Evasive Maneuvering 2
Evasive Maneuvering 3
Warp Drive Operation 1
Warp Drive Operation 2
Warp Drive Operation 3
Spaceship Command 1
Spaceship Command 2
Spaceship Command 3
CPU Management 4
Power Grid Management 4
Capacitor Management 4
Capacitor Systems Operation 4
Mechanics 4
Hull Upgrades 4
Shield Management 4
Shield Operation 4
Long Range Targeting 4
Signature Analysis 4
Navigation 4
Evasive Maneuvering 4
Warp Drive Operation 4
Spaceship Command 4
CPU Management 5
Power Grid Management 5
Capacitor Management 5
Capacitor Systems Operation 5
Mechanics 5
Hull Upgrades 5
Shield Management 5
Shield Operation 5
Long Range Targeting 5
Signature Analysis 5
Navigation 5
Evasive Maneuvering 5
Warp Drive Operation 5
Spaceship Command 5
Alpha Friendly
Spaceship Command 1
Amarr Frigate 1
Caldari Frigate 1
Gallente Frigate 1
Minmatar Frigate 1
Gunnery 1
Small Energy Turret 1
Small Hybrid Turret 1
Small Projectile Turret 1
Missile Launcher Operation 1
Rockets 1
Missile Launcher Operation 2
Light Missiles 1
Drones 1
Light Drone Operation 1
Mechanics 1
Repair Systems 1
Power Grid Management 1
Shield Operation 1
Science 1
Science 2
Power Grid Management 2
Power Grid Management 3
Capacitor Emission Systems 1
Missile Bombardment 1
Shield Operation 2
Drones 2
CPU Management 1
CPU Management 2
CPU Management 3
Sensor Linking 1
Target Painting 1
Weapon Disruption 1
Hull Upgrades 1
Hull Upgrades 2
Hull Upgrades 3
Alpha Friendly
Science 1
Science 2
Power Grid Management 1
Power Grid Management 2
Power Grid Management 3
Capacitor Emission Systems 1
Capacitor Emission Systems 2
Missile Launcher Operation 1
Missile Bombardment 1
Energy Pulse Weapons 1
Energy Grid Upgrades 1
Energy Grid Upgrades 2
Mechanics 1
Repair Systems 1
Shield Operation 1
CPU Management 1
CPU Management 2
CPU Management 3
Sensor Linking 1
Target Painting 1
Weapon Disruption 1
Shield Operation 2
Hull Upgrades 1
Hull Upgrades 2
Hull Upgrades 3
Spaceship Command 1
Amarr Frigate 1
Gunnery 1
Small Energy Turret 1
Small Energy Turret 2
Small Energy Turret 3
Amarr Frigate 2
Amarr Frigate 3
Amarr Destroyer 1
Amarr Destroyer 2
Amarr Destroyer 3
Spaceship Command 2
Amarr Cruiser 1
Gunnery 2
Gunnery 3
Medium Energy Turret 1
Caldari Frigate 1
Missile Launcher Operation 2
Missile Launcher Operation 3
Light Missiles 1
Light Missiles 2
Light Missiles 3
Caldari Frigate 2
Caldari Frigate 3
Caldari Destroyer 1
Caldari Destroyer 2
Caldari Destroyer 3
Caldari Cruiser 1
Heavy Assault Missiles 1
Heavy Missiles 1
Gallente Frigate 1
Drones 1
Drones 2
Drones 3
Light Drone Operation 1
Small Hybrid Turret 1
Small Hybrid Turret 2
Small Hybrid Turret 3
Gallente Frigate 2
Gallente Frigate 3
Gallente Destroyer 1
Gallente Destroyer 2
Gallente Destroyer 3
Gallente Cruiser 1
Medium Drone Operation 1
Medium Hybrid Turret 1
Minmatar Frigate 1
Small Projectile Turret 1
Small Projectile Turret 2
Small Projectile Turret 3
Minmatar Frigate 2
Minmatar Frigate 3
Minmatar Destroyer 1
Minmatar Destroyer 2
Minmatar Destroyer 3
Minmatar Cruiser 1
Medium Projectile Turret 1
Alpha Friendly
Science 1
Science 2
Science 3
Science 4
Power Grid Management 1
Power Grid Management 2
Power Grid Management 3
Capacitor Management 1
Capacitor Management 2
Capacitor Management 3
Power Grid Management 4
Thermodynamics 1
Shield Upgrades 1
Shield Upgrades 2
Thermodynamics 2
Mechanics 1
Mechanics 2
Mechanics 3
Jury Rigging 1
Jury Rigging 2
Gunnery 1
Gunnery 2
Weapon Upgrades 1
Weapon Upgrades 2
Weapon Upgrades 3
Shield Upgrades 3
Jury Rigging 3
Armor Rigging 1
Astronautics Rigging 1
Drones Rigging 1
Electronic Superiority Rigging 1
Energy Weapon Rigging 1
Hybrid Weapon Rigging 1
Launcher Rigging 1
Projectile Weapon Rigging 1
Shield Rigging 1
Armor Rigging 2
Astronautics Rigging 2
Drones Rigging 2
Electronic Superiority Rigging 2
Energy Weapon Rigging 2
Hybrid Weapon Rigging 2
Launcher Rigging 2
Projectile Weapon Rigging 2
Shield Rigging 2
Thermodynamics 3
Armor Rigging 3
Astronautics Rigging 3
Drones Rigging 3
Electronic Superiority Rigging 3
Energy Weapon Rigging 3
Hybrid Weapon Rigging 3
Launcher Rigging 3
Projectile Weapon Rigging 3
Shield Rigging 3
Weapon Upgrades 4
Advanced Weapon Upgrades 1
Advanced Weapon Upgrades 2
Advanced Weapon Upgrades 3
Shield Upgrades 4
Thermodynamics 4
CPU Management 1
CPU Management 2
CPU Management 3
CPU Management 4
CPU Management 5
Power Grid Management 5
Alpha Friendly
Mechanics 1
Repair Systems 1
Repair Systems 2
Science 1
Power Grid Management 1
Power Grid Management 2
Shield Upgrades 1
Shield Upgrades 2
Power Grid Management 3
Shield Management 1
Shield Management 2
Tactical Shield Manipulation 1
Tactical Shield Manipulation 2
Mechanics 2
Mechanics 3
Armor Layering 1
Shield Operation 1
Shield Operation 2
Shield Operation 3
Shield Compensation 1
Shield Compensation 2
Repair Systems 3
Shield Upgrades 3
Energy Grid Upgrades 1
Energy Grid Upgrades 2
Energy Grid Upgrades 3
Shield Compensation 3
Shield Management 3
Tactical Shield Manipulation 3
Mechanics 4
Shield Operation 4
EM Shield Compensation 1
Explosive Shield Compensation 1
Kinetic Shield Compensation 1
Thermal Shield Compensation 1
EM Shield Compensation 2
Explosive Shield Compensation 2
Kinetic Shield Compensation 2
Thermal Shield Compensation 2
Repair Systems 4
Hull Upgrades 1
Hull Upgrades 2
Hull Upgrades 3
Hull Upgrades 4
EM Armor Compensation 1
Explosive Armor Compensation 1
Kinetic Armor Compensation 1
Thermal Armor Compensation 1
EM Armor Compensation 2
Explosive Armor Compensation 2
Kinetic Armor Compensation 2
Thermal Armor Compensation 2
Shield Upgrades 4
Energy Grid Upgrades 4
Shield Compensation 4
Shield Management 4
Tactical Shield Manipulation 4
Mechanics 5
Repair Systems 5
Hull Upgrades 5
Alpha Friendly
Navigation 1
Navigation 2
Navigation 3
Acceleration Control 1
Evasive Maneuvering 1
Evasive Maneuvering 2
CPU Management 1
CPU Management 2
CPU Management 3
Propulsion Jamming 1
Propulsion Jamming 2
Acceleration Control 2
Afterburner 1
Afterburner 2
Afterburner 3
High Speed Maneuvering 1
High Speed Maneuvering 2
Warp Drive Operation 1
Warp Drive Operation 2
Warp Drive Operation 3
Signature Analysis 1
Signature Analysis 2
Signature Analysis 3
Evasive Maneuvering 3
Long Range Targeting 1
Long Range Targeting 2
Long Range Targeting 3
Propulsion Jamming 3
Acceleration Control 3
Navigation 4
Spaceship Command 1
Spaceship Command 2
Spaceship Command 3
Spaceship Command 4
High Speed Maneuvering 3
Target Management 1
Target Management 2
Target Management 3
Target Management 4
Propulsion Jamming 4
Alpha Friendly
CPU Management 1
Electronic Warfare 1
Electronic Warfare 2
CPU Management 2
CPU Management 3
Frequency Modulation 1
Sensor Linking 1
Sensor Linking 2
Target Painting 1
Target Painting 2
Weapon Disruption 1
Weapon Disruption 2
Frequency Modulation 2
Electronic Warfare 3
CPU Management 4
Long Distance Jamming 1
Long Distance Jamming 2
Long Range Targeting 1
Long Range Targeting 2
Long Range Targeting 3
Science 1
Science 2
Power Grid Management 1
Power Grid Management 2
Power Grid Management 3
Capacitor Emission Systems 1
Capacitor Emission Systems 2
Capacitor Emission Systems 3
Sensor Linking 3
Target Painting 3
Weapon Disruption 3
Frequency Modulation 3
Long Distance Jamming 3
Target Management 1
Target Management 2
Target Management 3
Target Management 4
Electronic Warfare 4
Signal Dispersion 1
Signal Dispersion 2
Signal Dispersion 3
Long Range Targeting 4
Capacitor Emission Systems 4
Sensor Linking 4
Signal Suppression 1
Signal Suppression 2
Signal Suppression 3
Target Painting 4
Signature Focusing 1
Signature Focusing 2
Signature Focusing 3
Weapon Disruption 4
Weapon Destabilization 1
Weapon Destabilization 2
Weapon Destabilization 3
Target Management 5
Advanced Target Management 1
Alpha Friendly
Gunnery 1
Gunnery 2
Gunnery 3
Gunnery 4
Surgical Strike 1
Controlled Bursts 1
Controlled Bursts 2
Surgical Strike 2
Trajectory Analysis 1
Trajectory Analysis 2
Motion Prediction 1
Motion Prediction 2
Motion Prediction 3
Rapid Firing 1
Rapid Firing 2
Rapid Firing 3
Sharpshooter 1
Sharpshooter 2
Sharpshooter 3
Controlled Bursts 3
Surgical Strike 3
Trajectory Analysis 3
Motion Prediction 4
Rapid Firing 4
Sharpshooter 4
Controlled Bursts 4
Surgical Strike 4
Gunnery 5
Trajectory Analysis 4
Alpha Friendly
Gunnery 1
Small Projectile Turret 1
Small Projectile Turret 2
Small Projectile Turret 3
Small Projectile Turret 4
Small Projectile Turret 5
Gunnery 2
Sharpshooter 1
Sharpshooter 2
Sharpshooter 3
Small Artillery Specialization 1
Small Artillery Specialization 2
Small Artillery Specialization 3
Motion Prediction 1
Motion Prediction 2
Motion Prediction 3
Small Autocannon Specialization 1
Small Autocannon Specialization 2
Small Autocannon Specialization 3
Small Energy Turret 1
Small Energy Turret 2
Small Energy Turret 3
Small Energy Turret 4
Small Energy Turret 5
Small Beam Laser Specialization 1
Small Beam Laser Specialization 2
Small Beam Laser Specialization 3
Small Hybrid Turret 1
Small Hybrid Turret 2
Small Hybrid Turret 3
Small Hybrid Turret 4
Small Hybrid Turret 5
Small Blaster Specialization 1
Small Blaster Specialization 2
Small Blaster Specialization 3
Small Pulse Laser Specialization 1
Small Pulse Laser Specialization 2
Small Pulse Laser Specialization 3
Small Railgun Specialization 1
Small Railgun Specialization 2
Small Railgun Specialization 3
Gunnery 3
Medium Projectile Turret 1
Medium Projectile Turret 2
Medium Projectile Turret 3
Medium Projectile Turret 4
Medium Projectile Turret 5
Sharpshooter 4
Medium Artillery Specialization 1
Medium Artillery Specialization 2
Medium Artillery Specialization 3
Motion Prediction 4
Medium Autocannon Specialization 1
Medium Autocannon Specialization 2
Medium Autocannon Specialization 3
Medium Energy Turret 1
Medium Energy Turret 2
Medium Energy Turret 3
Medium Energy Turret 4
Medium Energy Turret 5
Medium Beam Laser Specialization 1
Medium Beam Laser Specialization 2
Medium Beam Laser Specialization 3
Medium Hybrid Turret 1
Medium Hybrid Turret 2
Medium Hybrid Turret 3
Medium Hybrid Turret 4
Medium Hybrid Turret 5
Medium Blaster Specialization 1
Medium Blaster Specialization 2
Medium Blaster Specialization 3
Medium Pulse Laser Specialization 1
Medium Pulse Laser Specialization 2
Medium Pulse Laser Specialization 3
Medium Railgun Specialization 1
Medium Railgun Specialization 2
Medium Railgun Specialization 3
Alpha Friendly
Missile Launcher Operation 1
Missile Launcher Operation 2
Rapid Launch 1
Target Navigation Prediction 1
Missile Bombardment 1
Missile Bombardment 2
Rapid Launch 2
Target Navigation Prediction 2
Missile Launcher Operation 3
Missile Projection 1
Missile Projection 2
Missile Bombardment 3
Rapid Launch 3
Target Navigation Prediction 3
Missile Launcher Operation 4
Guided Missile Precision 1
Warhead Upgrades 1
Guided Missile Precision 2
Warhead Upgrades 2
Guided Missile Precision 3
Warhead Upgrades 3
Missile Bombardment 4
Rapid Launch 4
Missile Launcher Operation 5
Alpha Friendly
Missile Launcher Operation 1
Rockets 1
Rockets 2
Rockets 3
Rockets 4
Rockets 5
Rocket Specialization 1
Rocket Specialization 2
Rocket Specialization 3
Missile Launcher Operation 2
Light Missiles 1
Light Missiles 2
Light Missiles 3
Light Missiles 4
Light Missiles 5
Light Missile Specialization 1
Light Missile Specialization 2
Light Missile Specialization 3
Missile Launcher Operation 3
Heavy Missiles 1
Heavy Missiles 2
Heavy Missiles 3
Heavy Missiles 4
Heavy Missiles 5
Heavy Missile Specialization 1
Heavy Missile Specialization 2
Heavy Missile Specialization 3
Heavy Assault Missiles 1
Heavy Assault Missiles 2
Heavy Assault Missiles 3
Heavy Assault Missiles 4
Heavy Assault Missiles 5
Heavy Assault Missile Specialization 1
Heavy Assault Missile Specialization 2
Heavy Assault Missile Specialization 3
Alpha Friendly (except Medium & Heavy Drone IV & V)
Drones 1
Drone Avionics 1
Drone Avionics 2
Light Drone Operation 1
Light Drone Operation 2
Drones 2
Drones 3
Medium Drone Operation 1
Medium Drone Operation 2
Drone Avionics 3
Light Drone Operation 3
Medium Drone Operation 3
Drones 4
Drone Navigation 1
Drone Durability 1
Drone Navigation 2
Drone Durability 2
Drone Navigation 3
Drone Durability 3
Drone Avionics 4
Drone Navigation 4
Light Drone Operation 4
Medium Drone Operation 4
Drone Durability 4
Drones 5
Drone Sharpshooting 1
Drone Interfacing 1
Heavy Drone Operation 1
Drone Sharpshooting 2
Drone Interfacing 2
Heavy Drone Operation 2
Drone Sharpshooting 3
Drone Interfacing 3
Heavy Drone Operation 3
Drone Sharpshooting 4
Light Drone Operation 5
Amarr Drone Specialization 1
Amarr Drone Specialization 2
Caldari Drone Specialization 1
Caldari Drone Specialization 2
Gallente Drone Specialization 1
Gallente Drone Specialization 2
Minmatar Drone Specialization 1
Minmatar Drone Specialization 2
Medium Drone Operation 5
Heavy Drone Operation 4
Heavy Drone Operation 5
Omega Required
Leadership 1
Armored Command 1
Information Command 1
Shield Command 1
Skirmish Command 1
Armored Command 2
Information Command 2
Shield Command 2
Skirmish Command 2
Armored Command 3
Information Command 3
Shield Command 3
Skirmish Command 3
Armored Command 4
Information Command 4
Shield Command 4
Skirmish Command 4
Armored Command 5
Armored Command Specialist 1
Information Command 5
Information Command Specialist 1
Shield Command 5
Shield Command Specialist 1
Skirmish Command 5
Skirmish Command Specialist 1
Omega Required
Spaceship Command 1
Spaceship Command 2
Spaceship Command 3
CPU Management 1
CPU Management 2
Long Range Targeting 1
Long Range Targeting 2
Long Range Targeting 3
Long Range Targeting 4
Signature Analysis 1
Signature Analysis 2
Signature Analysis 3
Signature Analysis 4
Signature Analysis 5
Logistics Frigates 1
Logistics Frigates 2
Logistics Frigates 3
Logistics Frigates 4
Logistics Frigates 5
Long Range Targeting 5
Logistics Cruisers 1
Logistics Cruisers 2
Logistics Cruisers 3
Logistics Cruisers 4
Science 1
Science 2
Power Grid Management 1
Power Grid Management 2
Power Grid Management 3
Shield Emission Systems 1
CPU Management 3
CPU Management 4
Gravimetric Sensor Compensation 1
Ladar Sensor Compensation 1
Magnetometric Sensor Compensation 1
Radar Sensor Compensation 1
Mechanics 1
Repair Systems 1
Repair Systems 2
Shield Emission Systems 2
Gravimetric Sensor Compensation 2
Ladar Sensor Compensation 2
Magnetometric Sensor Compensation 2
Radar Sensor Compensation 2
Mechanics 2
Mechanics 3
Remote Armor Repair Systems 1
Remote Armor Repair Systems 2
Energy Grid Upgrades 1
Energy Grid Upgrades 2
Energy Grid Upgrades 3
Capacitor Emission Systems 1
Capacitor Emission Systems 2
Capacitor Emission Systems 3
Remote Armor Repair Systems 3
Shield Emission Systems 3
Gravimetric Sensor Compensation 3
Ladar Sensor Compensation 3
Magnetometric Sensor Compensation 3
Radar Sensor Compensation 3
Capacitor Systems Operation 1
Capacitor Systems Operation 2
Capacitor Systems Operation 3
Capacitor Systems Operation 4
Target Management 1
Target Management 2
Target Management 3
Target Management 4
Energy Grid Upgrades 4
Capacitor Emission Systems 4
Remote Armor Repair Systems 4
Shield Emission Systems 4
Capacitor Management 1
Capacitor Management 2
Capacitor Management 3
Capacitor Management 4
Capacitor Systems Operation 5
Target Management 5
Advanced Target Management 1
Advanced Target Management 2
Advanced Target Management 3
Shield Emission Systems 5
Remote Armor Repair Systems 5
Logistics Cruisers 5
2023.08.13 - Updated to match in game Skill Plans. Removed Shopping Lists
2022.05.28 - Removed references to Skill Queue limits and the Queue lists being smaller sized text
2022.02.20 - Fixed the T2 Drones section being duplicated in the T2 Missiles section
2022.02.13 - Added colors to "Alpha Friendly" and "Omega Required," fixed date of previous changelog
2022.02.05 - Document moved to Wiki and Changlog moved to bottom of document
2020.05.02 - Document Created