Baby Bath- Yes, you can shower with a baby. But you might find that little baby of yours licking up water, like ours did. So a small bath, or at the very least some type of mesh insert to put in a tub (if you are lucky enough to have one) is a must. Also one bottle of baby shampoo/body wash (not necessary, but probably good to have).
Swaddle blankets- We still swaddle every night! At the beginning it was a must because Baby Boy's hands would flail and wake him up. Now he still loves feeling bundled and sleeps a lot better with the swaddle. We love the Aden and Anais blankets for our summer baby, but again lots of types to choose from. Also regular blankets to put over the swaddle if it gets cold.
Cloud B Sleep Sheep- White noise was a big one for us, especially the first 3 months. After a while you get really tired of saying shhhhhh, over and over. This sheep is really cute, and we personally use the wave sounds to get Baby Boy to fall asleep.
Pacifiers- maybe you'll use them, maybe you won't. We only caved at around 2 months and Baby Boy just loves them and the sucking really soothes him. We've used Avent Soothies, Mam, and Nuk all successfully, but some kids are more picky.
Nightlight- because Baby will need to eat in the middle of the night...
Nosefrida- a contraption to suck out boggers. A lot better than the bulb if you have a snotty baby. We would always "de-boggify" before bed because young babies can only breathe through their nose, not their mouths.
A bed/crib- we used a twin bed stuck between our bed and the wall. This has made checking on the baby at night super easy (and we already had the bed, so it was free). Otherwise just get a crib.
(the far left is Baby Boy's bed, you can also spot the sleep sheep upside down)