It's going to differ for everyone, unfortunately. What is essential for some people is completely unnecessary for others.
A good example is honeybunmom's talk about baby needing more layers than you. That's not always the case. I once was at church in the middle of winter, and my oldest son, a preemie who was finally past his due date, started screaming his head off. I finally realized he was HOT. I had him in a sleeper inside our heated building. He was too hot. I changed him into a cooler outfit, and he was happy again. I got some nasty comments from older women afraid he was too cold, but he was comfortable. So be careful about judging other moms you see in the grocery store. Maybe their babies are hot natured like mine was.
Babies will tell you if they are not a comfortable temperature. My babies rarely use hats past the first few days after birth unless it's winter and they're outside. Being barefoot in the summer would be normal here. Socks get kicked off. If it was cold, I used a footed sleeper, usually a lightweight one that I could add a blanket to if necessary.
DSQ prefolds for burp cloths (my babies have all been heavy spitter uppers due to my overactive letdown)
Diapers (cloth or disposable)
A cheap manual breast pump for those times when baby sleeps all night for the first time and I wake up engorged and don't want to wake the nicely sleeping baby (hand expressing does not work for me)
Cheap bouncy chairs - just a safe place to put baby when I can't hold him, where my dogs and other children can't run over him
Good baby carriers (what you like will be personal preference, so attend a babywearing meeting and try some out)
A place to sleep (co-sleeping didn't work for us, so I use a pack-n-play with bassinet insert in our room the first two months, then move to crib in baby's own room when sleeping through the night... there is a wake-up period around 4-6 months usually, but I don't mind going upstairs for that)
Since baby is in it's own room at some point, a monitor is necessary to wake me up (or rather my DH nudges me, because I could sleep through a tornado)
A boppy type pillow makes nursing easier in the beginning, and DH uses it for napping with baby in the recliner
Oh yeah, a comfy recliner! Around 3 or 4 weeks old, my babies usually start getting reflux and need to sleep upright on my chest in the recliner. That usually lasts about 3-4 weeks.
Breast pads (cloth ones worked best for me), especially in the beginning
Cloth menstrual pads for the beginning (disposable give me rashes if worn more than 3 days or so)
Plenty of baby clothes, as you might have to change baby a few times during the day
A big enough purse or bag to hold diapers, wipes, and a change of baby clothes (always bring a change of baby clothes wherever you go!!! My oldest exploded all over his clothes and car seat on our very first outing, which was thankfully to the LC at the hospital, so they have me a cheap gown to change him into)
Car seat (I like infant seat for winter babies, because I can bundle them up inside, then run them out to the car and click it in... once it's warm, I leave the infant seat in the car)
That's all I can think of off hand. Those are all things I'll be getting for #4
, as I gave away all my baby stuff except my Babyhawk Oh Snap SSC. I plan to get maybe a shorty woven wrap as well.