@sparrowcloud,
On resolution: Your PS3 can broadcast at 1080p. The 720p picture will look fine, but you really won't be taking full advantage of the PS3 for game playing or blu-ray since it has a player built into it.
On supplier: Vizio is a decent, second tier supplier and they get fair to good marks from Consumer Reports. I don't see a reason to steer away from them since you aren't going to get a better brand at your price point.
On type: LCD uses less electricity (by a fair amount) than plasma. Most modern LCD tv's have resolved the issue with watching the TV from the side, but find one in the Wal Mart and look at it from a 45 degree angle. Make sure all the colors look right. Plasma is brighter and is subject to burn-in. If you leave your game on the splash screen and walk away, you might have a problem.
Given what you've written and your intended usage, I suggest the 1080p, LCD model. You will also want to buy an inexpensive HDMI cable (try newegg.com) to connect your PS3 to the TV. You can't transmit 1080p over anything else and store HDMI cables are insanely overpriced. Make sure the Vizio has HDMI inputs, although I'm sure it does on modern tv's.
Depending on your TV signal, you will need to have the right type of tuner to receive digital signals. Much of the "free" HD content you get on cable without paying extra for it comes in QAM format. If the TV has a QAM tuner as well as the standard HD tuner, that's a plus. If you are getting cable into a cable box, you might want another HDMI cable depending on your setup. If you are using an antenna, the standard analog and digital tuners in the TV should be fine.