Baby gear is such a crazy subject. My first and strongest recommendation is to take the hand me downs, take all the hand me downs. Sure, it's nice to imagine one of those picture perfect homes where all your baby stuff is gorgeous natural wood and white linen and your baby is always wearing clothes that are perfectly aligned with your aesthetic, and maybe if we had unlimited funds I would have been tempted to go that route (110%). But you use the baby gear for such a short window of time, in my opinion it's better to just use whatever motley collection of hand me downs you can get and realize that you really won't care, partly because you're going to be tired and partly because your baby is going to be so cute that it won't matter what color her play mat is. You're going to have to pass most of this stuff along within a year anyways and then you'll probably barely remember it. If you don't have a network of friends desperate to unload baby gear (not exaggerating - bins of stuff started showing up on our porch as soon as we announced I was pregnant - people want that stuff out of their house) but you want to save money then join a local mom's group on Facebook or troll Craigslist.
This post has affiliate links to Amazon, but if you have a good local store in your area (shout out to the Pump Station!) I highly recommend going there instead. Not only because you support them, but because it can be a huge source of support for you, and having someone to talk to and ask for advice is amazing in those first few weeks. That said, if your local options are limited or if getting out of the house feels unmanageable sometimes, most of this stuff is easily purchased online. I'm basically on a first name basis with the UPS guy now that I'm working from home and can't get out much.
We wanted to keep it fairly minimal, but here are the things we have ended up relying on:
Bassinet - they need a place to sleep. We use the SNOO. We've also used the Dockatot a few times because we got one from a friend. If we hadn't gotten the SNOO I probably would have gone with a simple basket set up, or a bedside "cosleeper" option. I'm not an expert here, because she's been sleeping with us the last few weeks at this point and I'm starting to wonder if I'll ever get her to sleep alone. (My first review of the SNOO is here, next update is due soon)
Car seat and stroller (duh) - we got a really nice infant car seat as a hand me down (only a year old) but I recently broke down and purchased a used car seat that was compatible with our stroller. Adrian hates getting in and out of her car seat, and it was making errands really hard. Being able to just pull the car seat out of the car and clip it into the stroller is amazing. I thought this was a luxury I didn't need, I was wrong. If possible, get a car seat that works with your stroller if you live somewhere where you're going to be driving a lot. We got the Cruz stroller (tip - look for the last year's model to save some money) and now have the Mesa car seat, which is great because you can wash basically all the cloth parts in the washing machine. If you're in a local mom's group on Facebook, car seats and strollers frequently pop up for sale. I wouldn't feel comfortable purchasing a used car seat on Craigslist (they expire and you can't use them if they've been in an accident) but I felt good about getting one because the mom's group is tight knit and I trust people in it.
Baby wrap - in the infant stage I find the wraps easier than the structured carriers, because it's more comfortable for wearing around the house. I got two of the Solly wraps because they seem to be the most lightweight, and we use them constantly. I actually got the second one a week after the first, because I was having trouble getting a chance to wash the first one because we used it so much. I wear her for several hours a day, both in the house and when we go out. She loves it (luckily) and I feel like it's our best bonding time. We also have an Ergo that we'll be using once she's a bit bigger.
Place to set baby down - our friend gave us this bouncer seat and it's been a lifesaver. She has no interest in sleeping in it like some babies do, but it's perfect for when she's awake and happy. She likes to sit in it while I work in the kitchen or shower. Side note - everyone raves about the Rock N Play, but I got one for free with points and she just isn't interested in it at all. Just a good reminder that babies don't all like the same things!
Changing pad with extra liners - we just used an old dresser as a changing table but we got a changing pad and some cute covers. I impulse registered for some of these changing pad liners, which you lie over the cover to reduce how often you have to wash the cover, and then we liked them so much we ended up ordering another set. I still love our changing pad and I'm bummed that we ended up needing to switch to the Hatch Baby Grow so we could have a scale (but I loooooove the functionality of the Grow - see my full review here).
Play mat - I didn't realize this was a thing, but our friends gave us their old one (similar to this one) and we use it all the time. It's nice to have a place for her to lie down and do tummy time and she really does love having her toys suspended above her.
Cheater swaddles - our bassinet comes with a velcro swaddle, so we use that. My sister used the halo swaddles with her kids and I liked those too. I know that it isn't hard to learn to swaddle them with a blanket, but I just have zero interest. I've already had to learn how to operate several bewildering pieces of baby equipment and that's enough.
Receiving blankets/swaddle blankets - despite not knowing how to swaddle I do use swaddle blankets all the time, mostly for breastfeeding or tucking around her when she's sitting in her bouncer. They are scattered all over our house, so I'm glad we have a lot in patterns/colors we are okay with. Personally, I prefer the swaddling blankets over the receiving blankets because they are bigger and lightweight so if I had to do it again I'd probably skip the receiving blankets. There are a million cute options out there, but you'll probably get a bunch as gifts anyways. If you want super soft and organic, we were given a two pack of the Wee Sprout brand and they are the softest, but you don't get the fun patterns.
Pacifier - opinions vary on this, but I was in tears during the first couple weeks of breastfeeding because we'd have 45 minute stretches at night where she was using my boob as a pacifier and I was in pain. I'd heard you had to wait six weeks to introduce the pacifier but our lactation consultant gave us the okay to go for it sooner. Of course, she didn't accept it right away but by four weeks it was my savior and I'm okay with it. She only takes it when she needs to go to sleep and it's easy to tell when she's hungry vs. when she only wants the pacifier. Our lactation consultant recommended using Soothies, but initially she wouldn't take those and we found that the Mam pacifier was the perfect gateway. After a few weeks with the Mam she graduated to the Soothie and now she happily takes it anytime she's feeling tired and ready to go to sleep. I also got a little pack of pacifier clips, which are critical if you don't want to have to pick the pacifier up off the floor a million times a day. (FYI - the reason I didn't stick with the Mam is that I found it harder to sterilize. Water would get into the nipple and it didn't seem to fully dry and one day I saw mold growing in it. I'm not sure if I was doing something wrong, but yuck. The Soothies are all one piece, so there's nowhere for water to get trapped.)
Clothes - footie pajamas and a couple hats. If you wanted to go super minimal, I think you could get away with a few sets of pajamas and 1 - 2 hats for the first three months. We are obsessed with the Cloud Island footie pjs from Target (pattern options change all the time, so that exact link might not work but just search their website). They come in packs of three, they're lightweight (pro for us, might be a con for you) and they have an inverted zipper, which is amazing for nighttime diaper changes because you don't have to fully undress them to get at their diaper.
Nursing pillow - I relied on the Brestfriend really heavily for every feeding the first few weeks but by two months in I was mostly just using it during the day and by three months I've stopped using it almost entirely. It does make breastfeeding much more comfortable in the beginning.
Nipple cream - so critical during the first weeks, now only used sporadically. They sent me home from the hospital with a tube of Lasinoh cream but my lactation consultant recommended this option from Motherlove because it's more moisturizing and I liked it better.
Hand pump - I got a free electric pump from insurance, but this Haakaa silicone hand pump is amazing for night time feedings. Adrian only eats one side during her early morning feeding, so my routine is to pop her on one side, then put the pump on the other. It is a simple vacuum system, so there's no noise and I just massage a little to help it out. It's surprisingly effective this way, although the set up takes a bit of juggling (let's not talk about the time she kicked the pump off my boob and I spilled four ounces of milk all over the bed and myself). It's a single piece, so cleaning it is so, so easy. I've been able to build up a freezer stash of milk this way too. (I didn't get anything fancy for freezing milk, I'm currently just using our regular silicone ice cube trays and then double ziploc bagging the cubes - UPDATE - I actually regret not just getting bags immediately. They are so much easier than the ice cubes and my daycare prefers them. I like the Medela ones best because they feel sturdiest and don't have weird flowers printed on them. We do use some of the ice cubes for teething but they're not convenient for bottles.)
Bottles - we started trying to get Adrian to take a bottle at 6 weeks, per the recommendation of our lactation consultant. It's been up and down. I've tried four different types of bottles and so far her favorite is the Nuk Simply Natural. She will also take the Comotomo, but those are three times as expensive and while I love how they look I hate how they tend to tip over. My only recommendation for bottles is not to register for a ton of one style, because you have no idea what your baby will take. If possible, borrow a variety from a friend, or just buy a couple to test out. We try to give her one bottle a day, in the hopes that she won't starve once she starts daycare. Some days are better than others, honestly. We don't use a bottle warmer, we just put some hot water in a cup and then swirl the bottle in it until it warms up. Works fine since we aren't heating bottles constantly.
Drying rack - I'm not sure if this is necessary but I like having a separate drying rack just for her stuff. Most of it is small enough that it would fall through our large rack, plus this seems cleaner. We got the Boon strip, which takes up minimal space and I think it's cute.
Diaper pail - we got this fancy Ubbi diaper pail and it does look nice and it works well. My sister happily used this much cheaper option, and as she wisely pointed out "No matter how nice it is, it's still just a trash can full of baby poop." I also have friends who avoided the diaper pail altogether and just made more frequent trips to take the trash out.
We did register for other little things - a forehead thermometer, hooded towels and washcloths, baby nail clippers, some rope baskets that we use for toys and laundry (separately). I got this back of the door storage organizer and use it to hold diapers, burp cloths, and other daily essentials, the stuff that you want to be able to grab quickly but don't necessarily have counter space for. I got a bath sling because it was cheap and simple and it's fine (I have this one but it cost $6 in store). Having some high contrast cards and books are nice, and I love these Wee Gallery alphabet cards in particular. A friend gave us this Silly Tails crinkly book and it's been a huge hit and I have to remember to take it with us everywhere.
What we realized we didn't need: a ton of clothes (as I mentioned, a few pairs of footed pajamas are probably all you need initially), a ton of toys, a full infant bath, a bottle warmer, a real changing table (dresser works fine). Probably a ton of other stuff that was on the recommended registry list that I'm currently forgetting.