These Skills are useful for any ship or profession and should be trained to IV as soon as you can :

Electronics (5 percent extra CPU/level)

Engineering (5 percent extra powergrid/level)

Energy Management (increases Capacitor capacity by 5 percent per level)

Energy Systems Operation (decreases Capacitor recharge time by 5 percent per level)

Mechanic (5 percent bonus to structure hit points per skill level)

Hull Upgrades (5 percent bonus to armor hit points per skill level)

Afterburner (10 percent bonus to Afterburner duration per skill level)

Navigation (5 percent bonus to sub-warp ship velocity per skill level)

Acceleration Control (5 percent Bonus to Afterburner and Microwarpdrive speed boost per skill level)

Evasive Maneuvering (5 percent improved ship agility for all ships per skill level)

Fuel Conservation (10 percent reduction in Afterburner capacitor needs per skill level)

Warp Drive Operation (10 percent reduction in the Capacitor need of initiating warp)

Spaceship Command (2 percent improved ship agility for all ships per skill level)

Weapons
Requires Gunnery II

Weapon Upgrades (5 percent reduction in the CPU needs of weapon turrets, launchers and smartbombs per skill level)

Train this to V, afterwards train

Advanced Weapon Upgrades (2 percent reduction in the powergrid needs of weapon turrets and launchers per per skill level)

to IV

Shield Tanking

Shield Management (5 percent bonus to shield capacity per skill level)

Shield Operation (5 percent reduction in shield recharge time per skill level)

Shield Upgrades (5 percent reduction in shield upgrade powergrid needs per skill level)

Armour Tanking

Repair Systems (5 percent reduction in repair systems duration per skill level)

Drones (can be used on most ships)

Drones (Can operate 1 drone per skill level)

Scout Drone Operation (Can use Light and Medium Scout Drones, drone control range increased by 5000 meters per skill level)

Note that while there are ways to affect your ships's drones abilities and the drone control range, there is no way to increase the bandwidth of your ship.

If you do missions you will get implants...