I did not have much for just after baby was born, for a variety of reasons, and I found that anything I didnt have was easy to get.
Carrier (I had difficulty using wraps and slings successfully when she was itty bitty) or Stroller
Cradle or Bassinet (worked until 3 months old), knit cradle or bassinet sheets
Changing Table (I use an antique of furniture that I already own), Changing Pad and Cover
2 receiving/swaddle blankets
2 Gowns and 4-6 Newborn Footed and/or onesies
3 bottles (she was exclusively bottle nursed/fed), I ended up getting four more bottles after birth
bookshelf, chest of drawers, or somewhere to organize clothing and or cloth if CD
trash pale or wet bag for dirty diapers or cloth diapers
baby hangers for the closet if using a closet
Swing (I bought a gliding swing when she was three weeks old, soothed her to sleep with late night fussiness)
Rocker (got when she was 4 weeks old, I wish I had looked into this sooner because most took 10 weeks to order and I wanted it NOW)
-but honestly didnt truly NEED it, but I love rocking her)
Crib (I bought the crib and bedding at 2 months old)
Musical plush toy or some type of music was soothing (purchased at 2 months old)
Of course, now I feel like I have bought out BOTH Babies R Us and Buy Buy Baby, but at first we were quite comfortable with these items, and did not feel under prepared.
I wound up using my Pack n'Play until my baby girl learned to crawl out of it at age 2.5. Those things hold up really well. The bassinet attachment made the immediate post-partum recovery period much easier - no bending over to pick the baby up or put her down (big deal if you're recovering from a c-section). I cannot say enough good stuff about them. You want some sheets, because they're easier to clean then the PnP mattress.
For a newborn, I did fine with the PnP (with bassinet and baby changer attachment), and a comfortable chair for me. If I could get just one other item, it would be a dresser, low enough that I could put a changing pad on it and change the baby there, because they outgrow the PnP changing station pretty fast. I have, however, had a lot more luck finding changing tables at the Salvation Army - people hold on to their dressers - and those are okay too, although once the babe starts crawling, they're not as useful for storage.
I second the idea of somewhere bench-height to change baby. So much easier than bending over a low bed or getting up and down from the floor all the time.
Mother of two spectacular girls, born mid-2010 and late 2012
Also, I mentioned the hoppy, but really a firm pillow will work just as well.
You don't need much investment... check out this great website: www.bedstart.com Hope it gives you some great ideas!
Happy housewife and mom to big Z, born at home 1/2012. m/c 07/14 @ 5w and happy to get back to trying!