1. Aden + Anais swaddle blankets - I know you've probably heard a lot about this but this list would be remiss without them. When Birdie was still tiny she didn't fit in #3 and these were a lifesaver. They are incredibly soft, light and breathable. But apart from swaddling I use them as burp clothes, to cover her in her stroller and often as a blanket. 
2. Badger Baby Balm - this stuff is fantastic. I used it on her bum since day one and she has never had a problem with diaper rash. I also use it for the myriad of random rashes that she gets every so often on her face and it will inevitably clear it up in a matter of 24 hours.
3. Miracle Blanket - so this... this really is a miracle blanket. We were able to switch V to this by the time she was one month old and I have been using it ever since. She never gets out of it and it works wonders at calming her down when she's really upset. It's also incredibly easy to use. 
4. Gerber infant onsies - these onsies were the only ones that fit her when we first brought her home. They're incredibly cheap (less than $10 for four) and you won't feel bad when they get stained. They are quite soft too, considering the price. 
5. Honest Company diapers - I can't say enough good things about this brand. The diapers are wonderful, the price is actually less than what you would pay at the store and they throw in wipes for free! Their service is fantastic too. For example, we have been having issues with V going #2 only once a week (thus we go through half the amount of diapers you normally would) and they had no problem switching me to an every 8 weeks schedule versus the normal 4 week schedule so that I wouldn't have to throw out the unused diapers.
6. Tommee Tippee bottles - these are the only bottles V likes since they do such a great job of imitating the breast. You will be using bottles even if you breastfeed for a variety of reasons so I highly recommend stocking up on these. I also really like the size and shape of them. I also purchased these bags for when I take her milk on the go.
7. Eco baby blanket - I adore this blanket from Giggle (they also have it in green). It's just the right size and thickness. It also has some stretch to it so it works well as a swaddle blanket. I use it day and night and take it everywhere with us. 
8. Safety 1st baby nail clippers - You may think it strange to list these as an "essential" but... 1) baby's nails grow so fast! b) having the right tool to cut the tiniest, flimsiest nails is key 3) the grip on these helps you get around those miniature fingers (which is oh-so-scary by the way)
9. Ubbi diaper pail - the price is a bit excessive but the fact that V's room does not reek of poo & pee is kind of worth it. It also brings to mind this genius Simpson's line: Salesman: "But surely, you can't put a price on your family's lives?" Homer:I wouldn't have thought so either, but here we are." Turns out you can put a price on your house not smelling like baby poo.
10. 3 Sprouts towel - it's cute, it's soft and it's extra thick. That's all I got for this one!
11. Natursutten pacifiers - I forget how I heard about this pacifier in the first place but it's orthodontic and is supposed to protect against "nipple confusion." We gave it to Birdie from the first day (in those tough first days it was often the only thing that would give us some peace and quiet) and I never had any problems with it. She's not dependent on it but it's helpful when putting her to sleep or calming her down. Also, full disclosure, it will garner stares.

I hope you find this list useful. I know I was stalking these sort of lists for months while I was pregnant and it really helped to know what we would need and what products were good. Also, if you would be interested in any more of these sorts of list (i.e., the bigger items, clothes, etc) let me know and I will put one together.