No you don't need a cot bumper, they aren't recommended. Some people use the airwrap ones. The lullaby trust has some good info on sleeping see here:
www.lullabytrust.org.uk/mattresses-and-bedding
I bought up to 1 month sleep suits and vests and 0-3. Didn't use newborn, DS would have grown out of them quickly. We bought size 1 nappies, but don't buy tons as you may find they leak and you want to change brands. I think we've used every brand of nappies in 3 years.
Hats are only needed for outdoors and scratch mits are useful or buy the sleepsuits (babygros) with the fold over cuffs.
You may find you're changing vests and babygros 3 times a day so buy at least 10 of each. They're cheap enough to buy, supermarkets do nice ones. We did bit a few more expensive ones from Next. Especially neutral ones as we didn't find out the sex either time.
Nappy cream, metanium is excellent for nappy rash, just apply a thin layer. Sudocrem is good too, they make a good barrier cream. I only apply cream when I need to.
If you're breast feeding then a supportive pillow is good, if not then first time round I bought a microwave steriliser and second time bought a Milton tank which was so much easier and less of a faff. Tommeee tippeee bottles were really good, still using them with dc2. I had a change mat for upstairs and down, I never bothered with a change table.
Don't forget that all supermarkets regularly have baby events so you will always find offers and things cheaper so don't panic too much, and you'll be given loads when baby is born.