Depends on your definition of essential. You can make do with alot of things.
A carseat if you've got a car.
A cot and bedding
Nappies, cotton wool
Nursing bras and phone number of support if bfing
Bottles, steriliser and formula if not
A few sleepsuits to get you started
A couple of hats
We bathed dd in a plastic crate we already had, or she came in the bath with me. We were given tonnes of johnsons stuff that I'm still trying to get through. You don't need it in the first couple of weeks, just water will do.
We changed on an old towel
Didn't need any extra clothes coz was bought shed loads.
I bought a breast pump when she was 4wks which came with its own microwave steriliser and bottles, wouldn't bother buying it in advance tho coz you don't know if you'll want it or not.
Lansinoh saved my boobs when bfing but at £10 a tube its an expensive thing to not need. (MW sometimes have little sample sachets if you're desperate)
Pushchair, think about what you're going to be doing post birth tho and get one suitable. ie if you walk a dog in woods daily you'll benefit from a robust off road type, but if you catch the bus into town and want to whip round the shops then a small lightweight one would be better IYSWIM.
A small bottle of milton or similar will see you though any sterilising emergencies and its handy for general disinfection that comes with parenthood.
Any old rucksack/large handbag will do as a changing bag.
Oh and check out the bounty website coz you get free samples of stuff when the baby is born, the little pot of sudocreme I got in there lasted me the nappy years and fitted in my changing bag beautifully.
Then after baby is born and you've worked out which way is up and sorted through what everyone has got you/baby.
A snow suit is handy
I liked having a moses basket, we moved it round the house with us and just took her up to bed with us when we went.