These were my essentials -
Cot/moses basket - moses baskets are very expensive for the amount of time you will use them, but if you get one second hand it will be invaluable.
Pram/car seat - one or both depending on whether you have a car or not
Sleepsuits, vests and socks
Blankets and cot sheets
All-in-one fleecy sleepsuit thingy, hat and mitts for outdoors
Nappies/wipes/cotton wool - you will need LOTS of these!
Baby bath - saves so much water
Sling - for getting things done when you have a grizzly baby
Dummy - I hated these things, but had two very sucky babies. You might find it useful. Try and get rid of it before they turn one though, or it's harder to get it off them.
7000 bibs - (ok, that's possibly a slight exaggeration )
Baby bouncer chair
Some interesting chewy/rattly/squeezy toys
Changing mat and very large bag