you need a minimum of 1 weeks supply so you're not trying to do washing/shopping in those first few days.
as a minimum I would say:
7-10 vests
7-10 sleepers/rompers
2 hats
2 pairs of mitts
2 cardigans
1 over-coat/snowsuit
I would get these in both newborn and 0-3 months - baby may not be in newborn long so you may need the 0-3s very quickly. If you want to be majorly prepared then get 3-6m too.
Nappies - allow 10 per day for the first 2 weeks, then you can drop down to 7 per day for the next 6 weeks or so. I tend to buy 4 packs of size 1s, 4 packs of size 2s etc, about 100 of each size. I do this because babies grow so quickly you don't want to be left with a stockpile of too small nappies. Wipes I would get 1 a week, or buy the offers when you can. You will need 1-2 packs per week, so a good stash is always handy. buy the sensitive ones and mix brands (same with the nappies - mix of brands is good) as you don't know if LO may not like a certain brand/type.
Muslin cloths!!!!! Cannot stress this enough. They are sooo useful for everything. Get at least 6.
2-3 blankets of different weights, 2-3 sheets for base of bed.
1 bottle of head to toe wash. You will not need this to begin with, but it's multi-purpose and will last for ages until you can get to know LOs routine etc.
Cotton wool - buy a big bag! lol It's useful for so many things and can be used by you too lol
Dummies, bottles and sterilising equipment - obviously these are up to you. Buy what you think you'll need but they're always in the shops so maybe put a £10/£20 note somewhere as just in case money for bottles, steriliser etc if needed.
You've now got the basics covered. Somewhere to sleep, something to wear, and something to eat. Everything else is up to you. A couple of things that I couldn't live without - bonjela and infacol. Brilliant for teething and colic, even from the early days so I always make sure I have these. Sudacrem is always on hand too! A good layer of sudacrem or vaseline (or another barrier, lanisoh is good) at every nappy change helps stave off nappy rash in the early days when their skin is still very new. Baby lotion/oil/olive oil can help with newborn dry skin too if you massage it in to chapped/cracked areas (most newborns peel after being in water for 9 mnths so don't panic).
I think that's it. Obviously there's the big things like car seat, pushchair, bouncer, bed/moses basket and eventually high chairs and bath seats. It's mindboggling, so don't let it phase you. Once you've made your list stick to it and you shouldn't find your budget sky-rocketing.
My other advice - stay on team yellow. Things are cheaper (strange but true) in neutral and can be re-used again and again!
Congratulations!
. W're using reusable nappies they come in some stunning colours and patterns but I'll also have a few nappies just in case. 
Never for a minute did I think you were ditzy - personally I think it's sensible to try to figure out what to prioritise.
