As the saying goes... you get what you pay for.
If you're buying under 42", 1080i or 1080p doesn't matter. The screens aren't designed to be different than 720p, so if you want to save money, get a 720p and you'll see it's every bit as crisp. Once you pass 42" though, then 1080i and the preferred 1080p come into play.
under 42".. LCD is your best bet for picture quality/price etc. Over 42", Plasma can't be touched for quality, brightness etc.
If you want to save coin, and don't want a plasma, try and find a LCoS screen. (Liquid Crystal on Silicone) The picture is unreal.
This is all very good advice. In addition, I would throw out these tips:
1) Consider your usage. 1080p is gorgeous... if you have it hooked up to 1080p equipment. Right now that consists of Blu-Ray and a small handful of cable channels. Everything else is 720p/1080i. So unless you plan on dropping another $200-$300 on a decent Blu-Ray player (along with buying all new disks) or happen to have an above-average 1080p selection from your cable provider, 720p/1080i will probably be just fine.
2) Contrast ratio. Pay attention to it. The contrast ratio is what makes a TV picture look bright and crisp. A bad contrast ratio can easily make a name brand 1080p TV look worse than an off brand 720p/1080i TV. Although the manufacturers can fudge the numbers a bit, its a good general guide to the quality of a TV.
3) Plasmas look great, but they've had a long history of wearing out before LCD's. For most of their history, plasmas had a life expectancy that was half that of LCD's. Though the manufacturers of the current generation of plasmas claim that they last just as long as LCD's, its impossible to know whether they're telling the truth.
4) Never buy off of specs alone. Go to a store and look at the TV you plan to buy. Compare it to similar TV's. Numbers can be easily stretched and product reviews misleading, but your eyes don't lie.