Overall rule of thumb: Babies need PEOPLE, not THINGS. That said, there are some useful tools that can make things easier.
A good quality baby carrier is a must-have. A stretchy wrap is a good, inexpensive choice for a newborn. Or a Mei Tai works well as an all-around good carrier. Ring slings or a proper fitting pouch is great for quick in and outs.
If you travel by car, you'll need a carseat. I do prefer the infant seats for the first few months, because the convertibles are a bit too big. My babies do much better in a convertible after about 3 months, though. They're more comfortable. Get a good quality convertible that will last for up to the highest rear-facing weight limits, and fit tall children. This will save money in the long run as you won't have to keep buying bigger seats... and keeping them rear facing as long as possible is MUCH safer.
If you have plans to use cloth diapers with wool soakers or longies, I'd actually recommend getting the wrap-around tshirts and long sleeve tshirts rather than onesies, because you really don't want to snap a onesie around wool. Shirts with really wide neckbands or better yet, wraps or buttons are best, as babies often don't like having shirts pulled over their heads, and you do a LOT of changing of clothes with a newborn.
You only need a small number of newborn clothes... get more items in 3-6 and 6-9 month sizes. Get a couple cute outfits if you MUST, but my babies always end up spending their whole day in sleepers... although this time, I think it will be longies and tshirts.
I would just choose one baby contraption to avoid clutter, my preference is a bouncy seat. It's easily portable and can be set on the bathroom floor while you shower. A small portable swing might serve the same purpose, but our huge swing just took up space (not to mention my older ones are constantly pushing the buttons and getting baby going too fast!) and was barely ever used through three kids. We're getting rid of it this time around. A moses basket could also work.
We also do like to have a bassinet in the early days. Every once in awhile I'm able to put the baby in it for a nap... and it works pretty well for a changing table.
Extra virgin olive oil or coconut oil for baby massages, or if they get some flaky dry skin. Wyleda Calendula oil is awesome for diaper rashes.
A large water glass or stainless steel bottle. Stay hydrated. Stay away from plastic. Quart-sized preserving jars actually work really well. Get one good stainless steel water bottle for leaving home with.
Easily grabbable snacks and drinks, a book, nursing pillow (or just a supply of regular pillows in different sizes), comfortable chair with a footrest, books or magazines, a queue of new shows/movies to watch (assuming first baby here... this part is different if you have olders).
Pump, bottles, accessories if you will be returning to work. If you're staying home full time, I've found them to be completely unnecessary. And I take breaks from my babies. When they're really small, dh can entertain them for a half hour to an hour so I can get a break. As they get bigger, I can take longer breaks. By a few months old, I can leave for 2 hours without needing to leave a bottle. My babies never even took pacis (although I tried really hard with my first, and a bit hard with my 2nd), and they did fine.
If you're using cloth diapers, I'd recommend a diaper sprayer attachment to the toilet. Not necessary, but very useful!
Hylands Colic and Teething Tablets, also gripe water (although the teething tablets won't be needed for a few months--stay away from baby orajel)
A vaporizer for those nights baby gets congested, or just to beat winter dryness.
I do use a stroller on occasion when babies are bigger.... like after 6 months. So, if you can get someone to buy you a nice stroller for a shower gift, go for it. They also work really well for carrying diaper bags and shopping bags. And make a great footrest for nursing. You can find really good deals on used strollers, though, and many brands hold up well over time. Just keep in mind your lifestlye. Make sure the stroller fits easily in your vehicle... or get a great jogging style one if you live in a walkable neighborhood.
Best luxury baby items of all: king sized mattress and a rocker... or actually I use our huge double-sized recliner the most.
Things I have found I DON'T need:
--a lot of baby equipment (a lot of clutter to trip over)
--baby bath products (stay FAR away from the conventional petroleum-based products.. there is some nice natural options out there like California Baby, but really, you just need a washcloth and warm water... bath products are just a waste of money.)
--changing table (the floor is safer anyways, just get a nice changing pad)
--any kind of noisy or light up baby toy, really anything with batteries (ANNOYING. My babies like to just hang out with me and watch the world. They do not need constant stimulation, they just need to be part of your everyday routine. Play real music for them, not the canned baby-toy/contraption crapola.)
--"baby" videos (I mean, really, WTF?)
--nursery furniture (you just need a drawer or two for clothes and a place to stash diapers)
--baby medications... they keep recalling these, anyways. We really don't know what's safe for babies... except breastmilk. Breastmilk works on just about everything (in the nose, eyes, on the skin, etc.)
--conventional diaper rash creams (do you really want to put steroids and antibiotics on your baby's private parts???)
--infant car seats used as baby transporters... those things are heavy and awkward to carry. And they do not put baby in best ergonomic position, not to mention the flat-head syndrome. And seriously, it is often way easier and faster to pop baby in a carrier than to open the trunk, drag out the stroller, lock seat in stroller, and then try to negotiate your way through a slushy street, or narrow aisles, etc. In many cases, big bulky strollers and infant carriers are just a hindrance. And for God sakes, if your baby is screaming in a contraption, you might want to try PICKING HIM UP instead of frantically shushing, rocking/pushing, and attempting to stuff a rejected pacifier back in his mouth for the 20th time.