This isn't quite as complex as it sounds. Some general tips will help:
The correct HD resolutions are:
720p = 1280x720 pixels, not interlaced (NOT 1366x768 - those sets have more pixels than 720p dictates, and thus must slightly UPSCALE 720p to display an image without a small black boarder - upscaling is almost always a BAD thing - see notes below)
1080i / 1080p = 1920x1080 pixels, either interlaced or not, depending on the "i" or "p".
And finally, it is always best to have a set which displays the exact number of pixels being sent to it. That is, if you have a 720p signal, you'll want a set that can display exactly 1280x720 pixels without any upscaling or downscaling. Unfortunately, most consumers don't understand this, thus most common 720p HDTV sets are now 1366x768 - because people automatically think that is "better," which means you get a worse display from a 720p source.
To see the problems I'm talking about with scaling, go to any computer with an LCD display and set the screen's resolution to anything other than the "native" resolution. Thus, if you have a 1600x1200 display, try setting it to 1280x960 instead. Notice that everything is much, much fuzzier?
But then it gets a bit more tricky, because DOWNSCALING - or reducing the number of pixels is much better than UPSCALING. So, the rule of thumb, if possible, is to match the EXACT resolution of your devices. So if you're playing nearly all 720p games, then a 720p set will be perfect for you - but be sure and buy one which can display 1280x720 pixels without scaling. You'll get a very small black bar on each edge of the screen, but your picture will be sharper. If, however, you want to get the best possible display Blue-Ray movies and those few games which do support 1080p, then go with a 1080p set. Also, the smaller your screen, the less difference this will make, so if you're buying a small set you'll probably be fine with 720p.
Some of the 1366x768 sets will allow you to display 720p at the native resolution rather than upscaling the image by 88x48 pixels. Be absolutely sure the set you buy supports this function if you want the best-quality 720p display.
Furthermore, some products have far better scalers than others. Do some research first and make sure that the scaling technology built into the set you get is a good one (unless you never intend to run it at any resolution other than the set's native resolution).
Hope that helps a little...