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For 720p (1280x720) a 1366x768 screen is just fine. Since most broadcast HDTV here in the US is either 1080i or 720p. Hardly anyone broadcasts 1080p since they can fit two 1080i or 720p stations into the same bandwidth. So for actually watching TV a 1366x768 set is fine, and most game consoles do better at 720p than 1080p anyway. I've been pretty happy with my 32" vizio for gaming, my Wii (480p only admitedly) looks great on it, and the 360 of course looks awesome.
However, for a computer monitor 1366x768 is kind of small, and 32" is kind of large. If you want to go the HDTV as computer monitor route, its probably better to save up and get a 1080p set. I did use mine comfortably as a computer monitor for a few months though, so it is possible if you're feeling poor. Also, the resolution is odd so it can take a little fiddling to get working. I had to browse the nvidia driver documentation to get it working in linux.
If your primary purpose in buying a TV is to watch hd movies, I suppose 1080p is a better option since both formats support it and thats what the movies are encoded for. However, if you're going to be doing that, you're probably going to want larger than 32", and you're also probably going to be spending significantly more than $500 for a TV anyway.