Nappies and clothes definitely (seriously, those little outfits are cute but sooooo rarely practical on a newborn. Vests and babygrows all the way).
Nappy changing equipment - nappy cream, cotton wool, nappy sacks (keep well away from baby), baby wipes
Muslins for feeding/burping
A safe place for baby to sleep - moses basket or bedside crib (or one of each so you don't have to move them round the house all the time)
An infant car seat - you can't take your baby home from hospital without one
Cellular blankets
Somewhere to put baby down - like a swing or bouncer. With the best will in the world you can't hold a baby all day every day. They are also sanity savers and allow you to have a meal/drink etc with baby within sight
One or two bottles even if you plan to breastfeed. I wouldn't get things like a breast pump in advance because in an ideal world, it's best not to pump in the first 6 weeks in MOST cases, to help you and baby work out the skill and establish a good supply in terms of demand
A pram and baby carrier if you want one. If you plan to put a newborn in a carrier, get one with head support. In terms of a pram, babies are better lying flat in a carrycot/bassinet for at least the first 5-6 months because progressing to the seat
Sterilising equipment. I've tried and tested and don't like steam sterilisers. They are quick and effective but require a lot more maintenance than a cold water steriliser. Cold water sterilisers need the water and sterilising solution changing every 24 hours, however
I think those are most of the essentials for now!