You can't go far wrong with sticking mostly to TIE fighters for the first few games.
Leave interceptors, bombers (and ordnance), Large ships (and trying to fly them round asteroids) and so on out for the first few games.
If you want to avoid just a cookie-cutter academy pilot swarm, I'd suggest using Vader and Black Squadron. You get a reasonable number of ships (but not too many), get to learn about pilot special abilities - but none are too complex, mostly extra attack dice - and you get to use Darth ******* Vader.
Darth Vader w/Engine Upgrade and Squad Leader
yes, it's an advanced. But it's also the best pilot in the game in a forgivingly tough ship, and teaches a player about "action economy" with squad leader in a nice, simple way.
Vader's canonical wingmen flight. Satisfy any potential nerd rage by not putting Howlrunner into the list. Besides which, Backstabber and Mithel make a nice paring; both get an extra attack die but in different circumstances. Makes for a nice educational exercise in piloting.
Black Squadron Pilot w/Veteran Instincts
For no better reason than it's a point and it makes everyone PS6 - which makes you better than anyone else's 'generic pilots' but worse than anyone someone with limited SW knowledge has ever heard of. Which again, feels right.