Unless you're a doctor or Howard Hughes, you're going to be washing your hands more often than you ever imagined possible when you bring a new baby home. So whatever soap you get, you'll be soaking in it. "In dishwashing liquid??" screams a TV voice from your childhood, and you wonder if you should get Palmolive. I have no idea. But Softsoap sure did give me dishpan hands after a couple of days. Pay attention to what they're using in the hospital and see if you can scam a bottle of that.
Also, even if you're a firm believer in the 10-second rule, you'll find yourself unable to practice it with a new kid, at least at first. Don't worry, there'll be time later. I guess.