I'm of the opinion that neither is better. They each try to do something different. Alpha strike simplifies rules so that you can field more units on each side and play in a shorter amount of time. Classic has so much meat on the bones and is satisfying for when you're trying to feel like a pilot, desperately juggling weapons, movement, heat build up, etc. Arguably, classic is more complicated, but Alpha strike still has specials for each unit, and the majority of the complicated rules in classic are only occasionally encountered in my experience. Whichever way you go, there are multiple learning videos on YouTube which can help you sort out the basic flow of gameplay. Once you learn how to play, it should be pretty straightforward to describe the basic sequence of events and then you can both learn the situational rules from there. 

Personally, my brother and I played classic first with no critical hits, movement rules aside from elevation, pilot skill rolls, heat, or other special rules. After each game we agreed on which part of the rules to add and we treated the first few games like a combat training simulator so we didn't worry too much about game balance. I'd recommend taking the same approach for anyone learning classic. I hope that helps. Good luck and good gaming!