Has anyone tried playing a game that consisted of just 1 core pack and one of each expansion packs? If so, how did it go? Was it fairly balanced or too one sided?

Just make sure both sides are 100 point squads.

That's about what we've got for our group at school here, plus a couple extra core packs people have, and it works just fine. I've never even played a game with or against more than two of the same ship other than TIE Fighters.