For a good source of information on A/V equipment check out.
http://www.avsforum.com/avs-vb/As far as 1080i, 1080p, or 720p, they are all considered full HD. the difference between the (i), and the (p) is how the image is scanned onto the screen. (i) is interlaced, in simplified terms that means the image is scanned every other line, IE lines 1,3,5...1079, then lines 2,4,6...1080, (p) is progressive the lines are scanned in order 1,2,3...1080.
The number in front is lines of resolution a 1080 set be it interlaced or progressive has more lines of resolution than a 720 set. LCD t.v.'s have to be run in their native resolution or at least one that is supported by that tv. So with a 720p set you would limited to a resolution of (1280x720), a 1080 set would be (1920x1080). Make sure it can be used as a computer monitor, some can't.
If you are just using the set to watch tv or movies then the difference between a 40" 1080 set and a 720 set past about 3' is not noticeable to about 99% of the people. If you want to use it as a monitor as well then I would recommend going with a set that is 1080p as well as has 1to1 pixel mapping, plus a decent responce rate. Also be careful when looking at contrast ratios, differant companies use differant methods to obtain these numbers so they are not consistant from one brand to the other. Sometimes not even from one model to the next within a brand.
The best thing to do is look at the tv in person, and play with the settings most display tv's have brightness maxed out. Also make sure that who ever you purchase the set from has a good return policy. Do your research all tv's have their pros, and cons. You'll be much happier with your purchase in the long run.