To be honest, some 'essentials' are 'essential' for some people and a complete waste of time for others.
For a newborn:
You need
(1) some means of transporting baby.
(a) If you drive or are driven by friends you need a car seat. If you only ever taxi or public transport you do not, although it would be safer to use a car seat in a taxi, and infant seats are easy to strap in with just a seatbelt.
(b) if you walk a lot, a pushchair or a sling. IMHO a sling is invaluable anyway as most newborns don't like being put down and a sling means you can carry/calm them while still having hands and not worrying about dropping them.
(2) somewhere for them to sleep
SIDS guidelines have them in a crib/moses basket in your room. You need a new mattress if you buy second hand.
If you are able to cosleep safely (no one smokes, no drugs, see other things online...), that's also an option. A cosleeper cot is useful in such cases, but not necessary, and you can bodge a normal cot to work instead, taking care there are no gaps or differences in height between the two.
If your house is big or on two levels, consider something for them to sleep in downstairs too, perhaps a second moses basket or move the existing one downstairs daily.
You'll need a blanket of some description (breathable and not too warm) or a baby sleeping bag (nnb, suitable from birth) to keep them warm.
(3) clothes for them to wear
Babies come out in all sorts of different sizes and shapes. Clothes are equally stupidly sized, different brands are wildly different. Don't buy too much smaller stuff as you may not use it and if you can resist don't wash / depackage too many things so you can return for a bigger size if you don't use it. Friends / family may also give you loads, especially if you know others who've had babies. Sicky babies can go through lots of clothes, non-sicky babies less so.
The 'rule of thumb' is 1 extra layer than you, but our first sweated if we tried that (and he was a December baby!) so that lasted less than a week. We weren't particularly fond of vests either as they were more of a faff than necessary.
Don't forget hats (although hopefully our babies are born in warmer weather :) ) and socks or footed sleepsuits/trousers. If socks, Trumpette (seem to be a shortage, hope they haven't gone insolvent!) don't fall off, or use sock-ons.
(4) things to catch the poo / wee
Nappies, reusable or otherwise. Don't buy too many of one type until you know they work for you otherwise you'll end up with loads of nappies that leak. A bin/wetbag to put them in.
Wipes, but at first cotton wool. Reusable wipes are fabulous IMO.
We didn't need any sudocreme or anything like that.
(5) feeding
(a) If you're intending to breastfeed, you need nothing extra for baby at first. Later you can consider expressing. If you're worried you may not be able to feed from the start but would still like baby to have breastmilk, you can get a pump, but most hospitals will help you out with pump hire if that's the case, and their kit is often more impressive / robust anyway.
(b) If you're intending to formula feed, you're outside my area of expertise....
(c) muslins to wipe up sick / drool / spillage. Again some babies are tidier than others. Ours was tidy.
(6) things for you
(a) Bigger, comfier underwear for post birth. It needs to accommodate the massive maternity pads, and not be too tight if you are sore/stiches. (also said maternity pads)
(b) Earth Mama Angel Baby 'bottom spray' (redundant if you have a c-sec) - this is expensive but I loved it and buy it for all pregnant friends (weird I know)
(c) Lansinoh nipple cream if you're intending to bf (although I bought two tubes last time and never even opened them, so perhaps just prep OH with where to get it from at any hour of day or night if you do need it rather than buy, as it was about £10 a tube last time I bought!)
(d) breast pads