I currently have the Core Box, and a handful of ally/villain expansions:

Han Solo, Chewie, C3P0, R2D2, the Royal Guard Champion, Boba Fett.

How useful are the other expansions though, either the ally/villain packs or the big boxed expansions. Would they get much use right now, or are those later ones really going to be more useful when we get more content in the app?

I think with the core is enough, but other expansions add new items but it's not necessary if you don't want. Until they don' t add habitats it even can confuse you a bit.

With the boxes you’d get additional heroes, supply cards, item cards, and new enemies to face (including the ones in the corresponding packs). You can get plenty of use out of them.

Ally/villain packs are a little tougher to gauge. If you have a box that corresponds with a given pack you really get nothing out of the packs other than the figure. The packs that don’t have a corresponding box (plus the ISB Infiltrators) makes those allies/enemies available. Each wave 7 pack also gets you a weapon.

Double post, sorry

Double post, sorry. My phones acting wonky.