FFIV:
Agreed - Red Wings would make for a good remix.

FFVI:
Devil's Lab, for sure. Contrasting S1999AD - I myself tried remixing Tina, but I find the melody a bit too slow for a dance remix. Setzer's Theme would be excellent, as well. Oooh, the Floating Continent too, and Kefka's Tower too! Oh man, this is like an amusement park...

FFVII:
Crazy Motorcycle, JENOVA, Still More Fighting, Shinra Company, Cosmo Canyon, Cid's Theme... if you manage Cait Sith's Theme that would be interesting.

FFX:
Agree with S1999AD - Auron's Theme would be totally badass. Otherworld... maybe. And you already have the Prelude mixed for you! You might be able to pull of People of the North Pole as well - but I wouldn't do it, as I love that song's quaint charm.

Those are the soundtracks I know the best (of course, excluding non-FF games). As far as legality is concerned, as long as you're not making any money for it or not claiming full credit for it, you should be fine.