congratulations! he is beautiful!
I dont have any kids, but in college I'm studying musical development in children from birth to high school!
Some of the best research, especially in the really young, has been done by Edwin Gordon, and what he calls Music Learning Theory.
A child's musical aptitude is continually developing from birth to about age 9. The best thing you can do for children birth-9 musically.. is to expose them to music. This can be music of any kind, but the best is singing. Think about music learning the same way you think about language learning. First, babies listen for a while. Then they start to imitate (obviously this process takes years). Then they can start to string together patterns, and read, and perform. Thats when a child can learn an instrument such as ukulele, piano, or violin.
So you should definitely play for your baby boy, but of course not only to help his musical development! Music is a great way to express emotion and I think that will feel really good to be able to share your emotions with your son. As far what to play.. I dont think that really matters. I dont think he's gonna look up at you and say "I hate this song. NEXT". haha. And yes you should be conscious of volume, but the ukulele isn't too loud of an instrument. If your concerned, then maybe don't us a pick, strum softly, or try finger-picking single not patters.
Best of luck to you and your son! I hope this turns out to be a great bonding experience and lots of fun for both of you. =)