When they're little, sing 'em what you like, with a little backup
Brian's baby is getting better musical exposure than mine ever did:
For an infant that you're trying to sing to sleep it really doesn't matter what you sing them, just that you're singing. My wife and I both sing songs that we know all the words to - mostly punk, heavy metal, and industrial. While some of the more mellow songs are appropriate I've found that songs with a fast upbeat pace don't really make a big differences.
If you can't always remember the words: Load songs onto your MP3 player and buy a cheap set of ear buds. Cut one of the ear buds off and stick the good one in your ear. Instant prompting and musical accompaniments that only you can hear while leaving your other ear free to hear your child.