I was planning on buying one beginners game to teach the rules. I was thinking of AoR. If you where going to pick one, which one would it be?

I recommend AoR as it's the most easy to structure. The PCs have superiors who'll give them objectives, after all.

The adventure in the AoR beginner box leaves a little less room to improvise than the EotE box, but the free downloadable follow-up adventure is excellent (have a look in Support > Player Resources for Operation: Shadowpoint). Probably my favourite FFG adventure so far.

I will second Col. Orange. Operation Shadowpoint is quite entertaining. Whisper Base and Onderon are wonderful locations.

Of the three, I think the Edge boxed set was the most clear, best laid out of the tutorial levels. If I was teaching the game to new people, that would be the one I used.

I have played all three. I'd say EoE. Mostly because that introduced me to FG