Like PeneloRatsbane said, it's alot of things.

I would say primarily it's a story of revenge. Barret's fighting for the planet against those who have taken it down. Cloud wants to make Sephiroth pay for everything he's done, as is Tifa. Sephiroth initially believes he's taking revenge for the Ancients. Cid wants to stick it to Shinra, as does Yuffie.

But alot of those motives become restoration, like you suggested. Cloud is, among many things, a reluctant hero who's motives become more of stopping Sephiroth than just some vendetta. Barret understands he can't save the planet permanently, but understands what has to be done, same with Red XIII. Vincent's trying to atone for his sins.

But yeah, there's so many things going on in the plot of FFVII it's really hard to pidgeonhole it as just one thing. It was alot of crazy ideas that culminated into one hell of a ride, especially playing it when it first came out.