I'd go hang out on Autopia for a while, and get a feel for what will and will not work. Plenty of horror stories of half-assed polish jobs. I've done well with an inexpensive polisher, but you can't buy skill.

Most on that site will recommend a good orbital polisher, such as the Porter Cable 7424 (do NOT confuse this with a cheap grinder polisher, such as this - the only thing they have in common is they look the same, but cheaper model only goes circularly, and not orbitally, and there's a huge difference), but it's more about technique than equipment. Read, read, and read some more. Then find a junk piece, and practice on it. Evaluate your work, then read some more and try to figure out how you can improve your technique.

I've polished glass, but I've also seen some horrible work by people who insisted on taking short cuts.

Rule #1: Use the least aggressive means necessary to do the job.
Rule #2: If it's going too slow, but you're still making progress, reread rule #1.

And remember, you're not going to be able to get into the corners with a machine, so you're going to have to work those areas by hand anyway.