the main thing to know is that p is progressive and i is interlaced. progressive means that the tv draws each horizontal line in a row, while interlaced draws every other line. progressive will end up with a clear, crisper image, while interlacing can result in flicker, unless you're dealing with static images.

for games or fast-paced movies, you want progressive, so even if you can go 1080i, you'd want 720p, unless you have the ability to do 1080p.