Welcome to the 7th gen section and congratulations on your purchase. The best place to look for a replacement dash would be at a wreckers, or from someone who is parting out their Corolla (there has been a few people doing that around here lately). I don't think it would be worthwhile getting it re-covered due to the costs involved, although there's no harm in getting a few quotes.
As for the removal/installation, it's easy enough to do without breaking anything. You'd first have to remove the stereo surround, driver's side dash vent, gauge cluster etc, but that's easy. The dash itself is held in by a series of clips and screws. As long as you don't forget where the screws go, you shouldn't have a problem.
I'd highly recommend that you purchase a Haynes manual for the Corolla/Geo Prizm. It's jam packed full of useful information, including how to remove the dash. If you can't get your hands on one and would like me to write out what it says in my one word for word then I'm more than happy to do so.
EDIT: Here's a picture I just scanned from my Haynes manual to show you the various locations of the screws and clips that hold the dash in place. The dash might be slightly different to the Geo Prizm but the screw locations should be relatively the same:
1993 Toyota Corolla
Linear Mode
