One of our favorite items were the little snap up gowns like the one baby O has on below. For newborns, this was a great second layer over a onesie or shirt to keep them warm and is also easy to put on because you don't have to worry about putting it over their head. Some people complain about all the snaps, but I didn't mind. The flip over arms to cover her little hands so she wouldn't scratch herself (and to keep them warm) was also nice. It was long enough to cover her feet so we didn't necessarily need to put socks on her. These also convert to rompers when they are a bit bigger, but we mostly used it in gown form.
Like many people, we were also fans of the little side-snap t-shirts. They were great to wear before the umbilical cord stump fell off in lieu of a onesie. Later on, they were also a great underlayer for extra warmth under the onesie. I preferred the long sleeve ones for this reason, and because they have the little flip up hand covers. We were able to use these longer than even the newborn onesies since they didn't outgrow here as quickly and were great for layering in the perpetually cool Pacific Northwest weather.
At our baby shower, we had our friends decorate onesies, which was a lot of fun. Even better, is to have them decorate onesies of several different sizes. That way you don't need to worry about them growing out of them before you can wear them all. I would say they don't need more than half a dozen or so in each size. (Of course, our little one didn't spit up much, so we don't go through them as quickly as some might.) I try to take her picture in each one as she wears them and send it as a thank you to whomever made it.
My sister, a post-partum nurse, suggested I get the "my brest friend" nursing pillow. The name kind of threw me off, but once she showed me how to properly position it, this was great to use when baby and I were both new to breast feeding. It's also supposed to be good for those recovering from a c-section, which I was at the time. It was convenient to be able to clip this on and then be able to walk around if I forgot something without having to re-position it. The one place this didn't work that well was in the nursery rocker, since it's kind of wide. This was definitely more comfortable to use on a couch. I bought a second cover for this, and did end up having to change it a couple of times after spit ups and diaper blowouts. Little O did outgrow this after a couple of months, so a used one might not be a bad idea since you can wash the cover.
the tub below. The sling was great for when she was really tiny, especially for sponge baths. Once the stump was off and the belly button area was healed, we stopped using the sling and sit her on the infant side, where she was able to lean back. This tub also happened to be the perfect size to hang lengthwise from the sides of our bathtub, which made it easier to bathe her.
Summer infant and Halo, because they were quick and secure. My mom gave us some and I also bought some used since they grow out of them so quickly. Little O would fight the swaddle initially, but it really did help her to sleep better since her random limbs flailing would end up waking her up.
vibrating bouncy chair, like the one below. The toy bar comes off, which makes it easier to take them in and out. She loved the vibrations and there were many nights in the beginning when she would only sleep in this. It's also easy to carry around the house so you can keep an eye on the little one while eating or doing housework. One of our friends, was kind enough to pass theirs down when they were finished with it. Otherwise, these are easy to find used, and don't seem worth it to buy new since they outgrow it so quickly. It's easy to remove the seat and throw it in the wash. The only downsides to this chair are that it's easy to forget to turn off the vibrating and we stubbed our toes on the wide base all the time.
a swing really helped him soothe the baby. (In addition to the other S's suggested by Dr. Karp.) This can be a lot bulkier than the chair above, but we were able to fit it in the nursery and used it to help her nap when swaddling and white noise wasn't enough. O liked it better in the position not shown below, where you can swing front to back rather than side to side. We took off the play console and she's never used it. They also make more compact versions of this that sit lower to the floor. I wouldn't spend the money to buy this new since it's only used for a short period of time. They are easy to find used on craig's list and easy to clean. I was able to wash the entire seat portion in the washing machine, as well as the toys on the mobile.