I would say most definitely play the first movement. I currently play this sonata myself and like it the best of all three movements. The second, although fairly beautiful, is just too short to stand on its own, and the third may be a bit too long and monotonous. The first is probably the best out of these, and fun to play to boot.
Yay for those parallel 8th note runs! When I first heard those two passages, I thought, "Oh man, there's no way I can do that with both hands," but now I can play it like nothing. I love the first movement of this piece. Like a lot of pre-romantic composers, I never liked nor hated Beethoven all that much until I started playing his pieces, and this was my first foray into his piano pieces. The first is definitely the best balance of slow, deep emotion and quick, exciting motion.
Play the first, you won't regret it.