This is our 3rd, but we have no baby stuff since its been 7 years so we are starting anew. But I know what we want and need and don't this time. Here is my list.
Needs: Diapers, clothes, swaddling blankets (miracle blankets are my favorite, I want 2 this time), boppy or other nursing pillow, moby wrap for newborn (ergo for older), diaper bag, good waterproof mattress cover (we cosleep), bouncy chair (no frills, and a model I can bounce with my foot, this was the only way I could sit down and eat a lot of times), burp rags, blankets, wash cloths and cloth wipes, nursing bras and nursing pads (most of the time I just stuffed wash cloths in there), nose frida or other snot sucker, baby finger nail clippers, diaper cream, coconut oil or other oil you like for skin/rash/meconium, car seat.
Other wants and things we will need later: pack n play, nice swinging baby gate for the top of our stairs, bibs, teething toys, stroller, high chair. I've never had a cold weather newborn so I kind of want one of those cozy things you can cover your car seat with, but I'm also not one to go out with a newborn a lot either so I don't know if its worth it.
Didn't need: most of the things, we had a swing - didn't use it, most of the baby toys we didn't use, things like the bumbo, baby play mats, etc I think are unnecessary, our son did use one of those jumper seat things a lot, we never used a monitor, my first would never take a bottle so pumping was totally out of the question. I expressed by hand the few times I needed a little milk for something. I liked the baby bathtub with the hammock in it, but its used for such a short time and its definitely not a must. So much just depends on personal preference and the personality of your baby too.