Everyone has pretty much given you good information... All you have to do now is pick out a sweet TV!
It is true that nothing is being broadcast in progressive format... Everything is still interlaced. But that doesn't mean you should get a 1080i over a 720p or 1080p. The technology is here to get a progressive HD television (and the prices are getting so cheap now!), so I honestly would not get duked into buying a 1080i because of smaller price tags.
I only scanned through the other posts quickly, but I didn't see anyone explain the difference between the progressive and interlaced formats. You definitely want the progressive HD tvs... 1080i (interlaced) essentially works with every other line of pixels working at the same speed to bring you your picture. When Group A of every other line of pixels is showing you the picture, Group B of every other line of pixels is getting ready to project the next image. It happens simultaneously and goes so fast that you'll never actually notice anything, but basically if you buy a 1080i, only 540 lines are working at once as opposed to a 720p or 1080p who's lines are essentially firing twice as fast which represents a better picture in the end. Hope I explained this as basic and smoothly as possible....lol
As far as plasmas and LCDs, the better brands of LCDs are so good now that you've got to be quite the HD guru to see a major difference. Plasmas' contrast ratios are still better but like I said, LCDs are damn good these days. The best brands for LCDs are Pioneer, Samsung, Sharp, (sony is wayy overpriced for what you get)...
I have the top of the line 32" Samsung. It's GORGEOUS! If you buy a 32" HD tv or smaller, there's really no point in going to a 1080p. Once you are at that small of a screen size, you really will not notice any difference going from 720 to 1080. For HD tvs 37" and up, I'd definitely say to go with the 1080p. You will absolutely see differences in the fine details at this large of screen sizes.
Like everyone else said, try to buy a tv with a DVI input. A lot of the Samsung models have it built in. If you can't find a tv with a DVI input--- no big deal. You can simply buy a DVI to HDMI cord to plug your computer to your tv. The cords are a little more costly but you can find them cheaper at newegg.com
Hope some of this helps!
Mitch