Probably the genre that I'm best at as far as actual talent and skill level go is music games like Rock Band. However, A - Those wouldn't be much fun to watch, as it's difficult to talk and give commentary while playing, especially if I'm singing; B - I've about played all of the good rhythm games to death, and C - most of the best games are on consoles, so it would be much more difficult to record.
I like RPGs a lot - all genres of RPG are fine, though I prefer open world RPGs like Oblivion to heavily story driven ones like Dragon Age. I also don't find FPSes, though I'll admit I'm not the best at them. I can usually get through them on Normal difficulty without much trouble, but that's about the extent of my ability.
Puzzle games are also fun, but I'm not sure if watching a LP of someone playing a puzzle game would be interesting at all, especially if you've played the game yourself and know the solutions.
Perhaps the best choice would be something like Mother 3 - somewhat story driven, but allowing for a good amount of time free-roaming, and with great characters and a good amount of humor. Of course, I doubt there are any games as fantastic as Mother 3 out there that I haven't played, but it provides a good example of a the type of game I think would work best.