Obviously, this is at the top of the list. Let's just get this over with. You need a carseat. Duh. You already knew that. I can't tell you which one, but I know some people who can help you pick one that will fit your needs! Now, moving on.
2. Prefold diapers, covers & cloth wipes
I say prefolds, because these are the most minimalist, trusty, least-fuss diapers to have. They are made of natural fibers, so you don't need a fancy cloth diaper detergent -- just something powdered. I used just about every cloth diaper type out there (except some hybrid brands) for four years and can say in my experience, prefolds are truly the most trusty diapers out there. My babies had less blow-outs in prefolds than any other type of diaper -- that includes pocket diapers, all-in-ones, and disposables. I freakin' love prefolds. And it's all this baby is going to wear, because I know they work. No poop roulette here.
Oh. My. Goodness. So many burp cloths. I'm pretty sure I had two dozen with both my kids and it still didn't seem like enough! My babies spit up... a lot. And once you use one, you don't want it hanging around for too long, getting all stiff and sour. You'll go through them like crazy. I love to embellish plain, old Gerber prefolds with a piece of fabric down the middle to make 'em fancy. (These are not diaper quality, just so you know.)
4. Newborn mittens
This is one thing I didn't even think about when River was born. Babies are born with weapons -- tiny, razor-sharp claws. Unfortunately, their victims are often their own delicate, soft faces. I had to send John to the store to get a pack of baby mittens. In the heat of Texas August, there was my tiny boy, in a diaper and cotton mittens. At least his pretty little face was unscathed.
5. Infant grooming/first-aid kit
I don't recall all that actually comes in a grooming kit, but I'm pretty sure I only used the nasal aspirator, nail clippers, comb, and thermometer. The little comb is great for cradle cap, and you will use that nasal aspirator (affectionately called the Snot Sucker in our family) until the kid is old enough to blow his own nose. The newborn clippers that come in the kit are super easy to handle without slipping and nicking your baby's precious fingers... for the most part. (Sorry, Austen.)
6. Some clothes, not many
Specifically, t-shirts and sleep sacks. If it's cold, footsie pajamas, a winter bunting, and a light hat or two. To me, the newborn period isn't time to dress up baby and make her look adorable. She's already adorable and there will be plenty of time for that later. I like keeping the first few months simple. Newborns poop so much and I don't want to change a onesie three times a day (or more!), but I love little infant t-shirts. Sleep sacks are also fantastic to have, so you don't need to cover them with a blanket at night. When we moved to Washington during the winter when Austen was 6 weeks old, all she really wore in and out of the house were footsie sleepers and little cotton hats. They are easy, cute, and warm.
7. Ring sling
There are so many different kinds of carriers out there, it can be overwhelming. But this is supposed to be a minimalist list, not a confusing list! Ring slings don't require any special learning curve or talent. It took me about three tries before I felt confident wearing Austen, and after that it was bliss! I loved my ring sling; I wore her all the time. It was a life-saver, as mommy to a newborn and rambunctious two-year-old. And another reason the ring-sling makes this minimalist list is because of the price. Other carriers can cost about $100 or more, but you can buy a ring sling for about half that price. And if you have any amount of sewing machine skills whatsoever, you can also make your own ring sling. It's one of the easiest things to sew. And then when people ask you where you got that beautiful carrier (because the fabric you picked out was not only on sale, but also totally unique and gorgeous, you frugal, artsy mama, you) you get to sound super impressive when you say, "Oh, I just whipped this up over the weekend!" No one has to know it took you 15 minutes and cost only $20.
8. Swaddle blankets
I didn't have swaddle blankets with River, but ohh how I wish I did. Austen spent about 75% of the first two months of her life swaddled up nice and snug, using Aden and Anais blankets. But here's some more good news -- while those name-brand blankets are pretty pricey at $35, you can buy your own cotton gauze or muslin fabric for as little as $2 a yard, and then dye it whatever color you want. Then go crazy and potato-stamp some cute stars on it or whatever. (Like I said, frugal AND artsy, right?)
9. Coconut oil
Coconut oil can be used for so many things: a gentle, completely natural, not to mention antimicrobial and antibacterial diaper rash ointment (that is safe for those cloth diapers), a thermometer lubricant, a lotion, and cradle cap cream to name a few. I love coconut oil probably as much as I love swaddle blankets. And almost as much as I love ring slings. The awesome thing about coconut oil is that you use so little of it. A jar could easily last you a year or more. The stuff is amazing.
Teeny tiny baby socks, what is cuter! Except your actual baby, of course. I don't think you can have enough newborn socks. For starters, you'll loose them like they're going out of style. Baby will kick them off, they'll get eaten by the dryer, and it will be impossible to keep up with them because they are so damn small. Second, socks will help keep Baby at the right temperature. Although River was born in August in Texas and he spent most his day naked, I almost always had socks on him. His little toes would get cool to the touch. And of course, if your baby is born in the cooler months, socks are helpful for obvious reasons.
11. Thick, cozy blanket
Okay, we all know we don't put newborn babies to bed in thick, cozy blankets, right? Right. Thick, cozy blankets (like a crib comforter) are excellent for going out of the house and snuggling them in the car seat, wrapping Baby in your arms, or laying across their little bodies while they sleep under your supervision. As River got older and mobile, I found that I could nurse him to sleep in my arms wrapped in a thick blanket cradling his head, then move him to the bed without waking him, because the blanket kept his head from rocking back and forth and waking him up. Thicker blankets are also handy for playtime on the ground.
12. White noise
I don't necessarily mean a white noise machine -- anything that has the ability to make a loud, constant whooshing noise will work. A television on the wrong channel. An old radio. Your vacuum cleaner. A CD of ocean or rain sounds. Babies have spent the first nine months of their existence in fluid movement, listening to the loud, whooshing sounds of your heartbeat, the pulsing of the placenta, and the soothing, muffled sound of your voice; the world is just too quiet for them. Sometimes white noise was the only thing that would get Austen to stop screaming when she was a newborn. We'd turn the TV on extra-loud and she'd quiet down. It got really old listening to it for hours (yes, hours), but it wasn't as bad as listening to the heart-wrenching screams of a newborn babe. When she got a little older, we found a two-hour video of a waterfall on YouTube, and she listened to that to fall asleep until she was about nine months old.
13. A bag for diapers
And not necessarily a diaper bag! You could use a tote or a large purse. I got over my diaper bag pretty quickly when River was an infant. I found it much more useful when I had two children because I had more to carry around, but even then, often I'd just take one of my big purses. Unless you're planning to be away for hours, leaving the house with Baby doesn't have to be stressful -- a couple diapers, a change of clothes, a blanket, and you're set.
That's the Super Minimalist List, but personally, I would like to add a few other things I find helpful.
Neither of my kids took a pacifier. River kinda liked his until he was about six months old, and Austen straight-up refused one. I am tired of being a walking pacifier, y'all. Yes, mothers are the original paci, but sheesh, no one mentions how exhausting being the paci is! (Hint: it's really exhausting.) With two other kids to take care of, I really want to option to put something other than my boob in this baby's mouth so I can get things done. Dear Baby... please like pacifiers!
Oh precious swing, how do I love thee? Let me count the ways! If there's any major baby gear you should get, it's a swing, and you can probably find a used one for $30. When you need to get stuff done, good luck trying to lay your little one on a flat, unmoving surface. This is why swings are so awesome. But make sure you get one that actually works well -- Austen was so chunky, the swing my parents bought for her barely grunted back and forth under her weight! I could have done an underdog at the heights River's swing reached. Got him to sleep every time. Kept him asleep for 25 minutes. Which was as long as he ever slept. Ever.
16. Glass bottles
I prefer glass, because it's free of chemicals, and also because you can put it directly in boiling water to warm frozen milk. Of course, not everyone is going to need bottles. Austen wouldn't take a bottle at all, because I waited too long to give her one, so I plan on giving this baby a bottle a few times a week starting at about three weeks old, assuming breastfeeding is going well.
17. Infant bath sponge
Newborns need sink baths. It just makes sense. Tiny baby + sink = adorable. A bath sponge will give them a soft surface and help you feel less at risk of your slippery baby wriggling his way out of your hands, and you won't have to crouch over that clumsy infant tub that will only last them until they're six months old and they decide it's a great idea to try to climb out any chance they get.
18. A pack of disposable newborn diapers
One word: meconium. If you are planning on using cloth, this is not essential, but helpful. Meconium is dark, sticky, and will stain anything it touches, including your clean, pretty prefolds.
Austen didn't have a highchair and we survived. Though, I'd like to have one for this baby, to at least try to keep the food contained in one specific area.
I loved having an exersaucer for my babies. We bought Austen's used for $7, and gave it to her for her first Christmas! Many babies can start using them when they are about two months old, and can use them up until the time they start walking. The reason this makes the list is because most infants get to a point where they want to sit up and see the world and use those neck muscles, and they just can't do that lying down, even on a raised surface. An exersaucer also offers a safe, fun place for Baby to hang out when they get older.
One of my life rules is to always buy used if possible. You end up spending about a fourth of the price, and it's just gentler to the earth. Babies don't have to be expensive! And it's not a big deal if getting everything on a typical baby list is not realistic -- it wasn't realistic for us when River was a baby, and everything turned out fine. When Austen was born, I actually didn't want all the extra stuff. All we had for her were some clothes, blankets, diapers, and a diaper bag. Really! It wasn't until she'd been around for a few months that we got the used exersaucer and my parents bought her a swing. And babies don't need toys; you will find they are much more interested in things lying around the house, anyway. For the amount most baby gear costs compared to the length of time you actually use them, it's just not worth it to me. I didn't find parenting any easier when I had lots of baby gear compared to when I had just what we truly needed.