32" is right around where 1080p becomes relevant. If you will be sitting a fair distance (more than 2-3 meters) away from your TV, 720p will be fine, if you're getting right up in it's face, you'll want a better resolution.
The only difference between LED and LCD, as others have mentioned, is simply the backlighting technology. A true backlight grid will, theoretically, be better able to represent true black as the backlight can dim in black areas, and better represent darkness than a CCFL or Edge-Lit LED LCD tv.
TL;DR, if you're sitting far away and you're on a budget, just pick yourself up an el cheapo 720p 32" vizio, it'll be fine. If you're sitting close or want to splurge, invest a bit more, it'll be worth it.