1. Bassinet. Preferably one that vibrates. It put him to sleep every time.
2. Pacifier. This was a LIFE SAVER in the beginning. He's not as interested in it anymore.
3. Sound machine. One of the keys to putting him to sleep through the night.
4. Changing mat/ blanket. Since we don't have a changing table (which I would love but we have no room for) the next best thing is a "changing blanket. It's just a thick blanket we put down before we change him, because he pees on EVERYTHING!
5. Chair. When he wasn't sleeping in his bassinet, he was in this chair! Wonderful!
This is pretty much our essential list other than the things you need to feed and change him. We give him a shower with dad so we hardly used the bathtub but I imagine we will once he's able to sit-up.
Some of the things that would have been nice to have:
Wipe warmer. The cold wipes make him pee.
Bottle steamer. Washing bottles is the opposite if fun.
Swing. We borrowed a small swing when he was about two months, but it could hardly push him. Jed is 14 pounds of pure muscle.
I think the list is different for everyone but these are some of the things that helped us.