As far as the TV reslolution goes, unless you have one bigger than 50 inches its very difficult to see a difference between 720p and 1080p, both would look just as nice on a 32 inch. But as far as output from your pc, that will depend on your video card.
Just make sure to check the max resolution output on the video card you are looking to buy and compare it with your tv's resolution. Most newer video cards will be able to support well over what your tv will.
