1080p or 720p depends on the size of the TV you wish to purchase (i'm not gonna comment on LCD or plasma because I dont' think I know enough, i got LCD by the way). If you are purchasing anything less than or equal to 32 inch I dont' suggest you spend the extra to get 1080p, hell i doubt you will even find any brand name TVs that support 1080p on smaller screen size anyway. I have a 40 inch and so I chose one with 1080p, even then I can't see a difference between 720p and 1080p when playing video games, movies is more obvious though. And if you buy up to 50 inch, then the difference should be even more obvious.
If you have money to spend, getting TV that support 1080p is better obviously. Search Google for pros and cons between the LCD and Plasma, as there are a couple of advantages over the other. - Dynashox -
Plasma still hasn't been perfected. I'd say LCD every time. 1080p if you can afford it, if not 720p is fine.
As said by members, both LCD & Plasma have advantages and disadvantages over each other. However, what i have observed, 1080p does pretty well and watching dvd on LCD is also quite good. So i will go for an 32" or more LCD with 1080p.