For me what was esential, I am sure it is different for everyone, were
onsie undershirts
sleepers
Large size recieving blankets
a couple of nice outfits for going out
cradle swing
playpen in my room (crib we used later in baby's room)
baby bathtub
small washclothes
washer and dryer!!!!
mobile
socks to use as mitts to keep the baby from scratching. They stay on a lot better than the real mitts
hats
diapers
vaseline
zinc cream
wrap to carry baby in
that is all that I used the first month. I had just myself and my husband to help after my mom left the first week. You don't really need a lot. There is so much stuff you can buy that ends up being usless. Like for me, I never used the monitor I bought because I could here every sound and couldn't sleep. If the baby cried I could here it without the monitor as his room is right next to mine. Baby went to his own room at 5 weeks.
Editted to add
For bedding I use the crib sheet and light blanket. Once baby is older and moves, I use a grobag. That is all I have in the crib.
Feeding, I did use some breasts pads the first month for leakage. Baby doesn't take a bottle,or soother, so no advise on that aspect of feeding
These are the things I bought and never used,
soothers and the things to attach them to clothing
, breast pump, rarely used,
a few bottles and nipples,
monitor
bouncy chair
jarred baby food and baby cerals (baby refused them)
sippy cups with valves in them