So you want to participate in the AT and need skills. Here's a quick rundown of key skills needed and groups of skills.
Armor: All subcapital skills excluding remote hull repairs, get those compensations to V
Drones: Everything excluding fighters, mining, and mutated drones (some argument given the lack of t2 damage drones in the rules that specs arent needed)
Electronic Systems: If you want to be a control pilot then anything related to strength must be V and capacitor is secondary at V.
Engineering: Everything! Thermo V is mandatory
Fleet Support: Commands and Specialists including Fleet Command to V if you want to run any links.
Gunnery: This will be a ton of SP, get all subcapital weaponry to minimum Spec IV and start working on spec V's for weapon systems you'll commonly use.
Missiles: Same as gunnery.
Navigation: All non-jump related skills V, micro jump drive operation can be important
Neural Enhancement: Cybernetics II for x03 implants. Cybernetics V if you run links for mindlinks. Jump Clone skills to allow multiple clones
Rigging: Everything other than Jury Rigging itself to V. Many fits require maxed rig skills and the drawback reductions are significant.
Shields: See armor
Spaceship Command: Make sure all of your t1 and t2 ship skills are maxed to V for any ships you'll be looking to fly.
Subsystems: Get all these to V
Targeting: Everything to V except Advanced Target Management to III.