Another possible problem is that a lot of TVs use an overscan image - that is, the image spills off of either side. You can usually configure it to look right though.
And if you're using it as a monitor, I'd definitely say you'll want a 1080p LCD. LCDs have the sharpest, most defined pixels, and 1080p is way more useful than 720p for use as a monitor.
I have a 32" 720p LCD and I'm happy with it and I even use it as a monitor sometimes, but it's not good enough to use full time.