I know there are a million of these lists out there, but I thought I would add my two cents to the internets. Obviously every list of 'essentials' is going to be different because every baby is different. Everett doesn't take a pacifier or a bottle so those are not on our list, but if he did I am sure they would be essential. We didn't go too crazy with baby gear and we bought a lot of stuff as we learned and he grew and saw what he wanted/needed. Here is what we loved from 0-3 months.
1) Aiden and Anais Swaddle Blankets. Everyone recommends these, everybody has these and there is a good reason, they are perfect for swaddling, breastfeeding under, and even just as a light stroller blanket. We use them every single day.
2) A swing. Everett adored his swing, and took most of his naps in his swing for the first three months of his life. He liked to feel snug and loved the motion (especially as a colicky baby) We loved our Snug-a-bunny swing and never had any problems.
3) A Play Mat. When Everett was a little over a month, we sensed he needed a little more stimulation. His play mat gave me a good 10-15 minutes in the morning where he would lay and play on his mat so I could eat some breakfast or something. As he got older, he did all his tummy time on here and still loves to play on it. We just bought the cheapest one at Babies R Us and it has worked great!
4) Hands Down our most used, most recommended, can't live without baby item. Our Fisher Price Rock and Play. Not only did Everett refuse to sleep anywhere else but here for the first 3-4 months, but we used it all over the house, in the bathroom while I got ready, in the kitchen while I cooked, brought it to friends house while we played games. It is super light and portable, super comfortable for the baby and even at six months we still use it every day (not for sleeping anymore) but to keep him in one spot while I do something!
5) A good breast pump. I remember the night my milk came in the day after Everett was born, there was nothing I wouldn't do or pay for a breast pump! I tracked some lady down off Craigslist (stores were closed) and it was sweet sweet relief because my poor jaundiced baby did not have enough of an appetite. Mine unfortunately broke, but my awesome cousin Kristy has let me borrow hers, and hers is even better! I have tried a crappy cheap pump and there is such a difference. Even though Everett doesn't take a bottle, I still pump quite often to increase my milk supply, empty when he sleeps for longer periods and also store milk just in case he decides to bottle feed one of these days. I highly recommend a good pump like this Medela one. It is an investment but I think worth it.
6) A baby carrier. We just recently bought ours, but I so wish we would have had it sooner, even when E was just a newborn. I know most people love the Ergo but Everett only likes facing out, so we went with the Bjorn Active, and although my shoulders do get sore after a while, we love it and so does Everett!
7) A+D Cream. My favorite diaper cream by far. We tried all of them and this one goes on the smoothest, doesn't smell when they pee and works awesome for prevention and cure of diaper rash. We use this every time we change his diaper and have a tube in his diaper bag, and every room in the house.
8) A Pack and Play with a bassinet insert. We wanted Everett to sleep in our room until he was at least 6 months so he slept in the bassinet part and it has been great, because we didn't waste money on a separate bassinet that he would grow out of after three months because I know we will use the pack and play forever! Ps-contrary to popular belief the bassinet insert is just the same pack and play mattress elevated to about halfway up the pack n play. Ours also had a changing table insert, which I thought was the bassinet at first.
So Everett was of course a really colicky baby. I read article after article, all the colic forums and not only was the education and support helpful but we did find some things that worked for us, and believe me we tried everything.
1. An exercise ball. I read online somewhere about bouncing on a ball and it helping someone's colicky baby. One weekend we were in St. George helping Ben's mom move and she had an exercise ball,I thought why not and tried it, and it really did help Everett so much. Apparently it reminds them of how it felt when in the womb while the mother is walking? We just had to squeeze him tight, bring him in close and bounce.
2. These are especially awesome for colicky babies. Swaddle, swaddle swaddle.
3. A lot of times there was really nothing I could do to help Everett when he cried all day/night which was SO so hard. So sometimes, so I didn't go crazy, I would just sit and bounce him, turn on Netflix (with subtitles due to the crying) and distract myself....and bounce...It actually really helped. I watched all 9 seasons of Greys Anatomy (for like the fifth time) in the first three months of his life HA!
4. Gripe Water. My mom smuggled this stuff into the States for me from Canada, and although we don't know if it really did work, he did calm down initially right when we gave it to him. It apparently used to (and still does in Europe and stuff) have alcohol in it but not in the US or Canada anymore...too bad ;)
5. Probiotic drops. Our doctor recommended we try these because Everett always seemed to have an upset stomach, and I think they helped. They made him more regular if you know what I mean and even though his poops smelt like yogurt on these, I would highly recommend them for a baby with stomach pain/colic.
6. This book. When I first read it, I was a sleep deprived crazy zombie and do it didn't make much sense to me but now re-reading it as we are sleep training Everett there is so much valuable info in there, and he is spot on when it comes to colicky babies, I honestly felt like I was reading stories about Everett. There is also a lot of information for sleep for post-colic babies which has been really helpful.
Johnson's baby wash and baby lotion. I know there is all this healthy organic chemical free stuff but I am such a sucker for that traditional Johnson's baby smell.
Dohm noise maker. Best, most not-annoying noise maker there is.
A glider-loved rocking and nursing Everett in ours, I am pretty sure my butt is permanently molded into the cushion because I spent so much time on that thing
Some stuff we probably didn't really need.
Diaper Pail-his poops don't really stink at this point and we empty our regular garbage like once a day anyways.
Crib? Well we needed it eventually but for the first bit he just slept in the bassinet and we are just barely starting to transition him to his crib now (at 6 months)