Get a bit more of a buffer in savings to ease your mind and start doing the maths now.
Prams/ cots and the like can be bought second hand on Ebay or local selling sites for not a lot. Conversely they can also be bought for eye watering amounts.
Have a look around and see whats available.
Never buy a second hand car seat or mattress.
As a rough guide moses baskets last till they can pull themselves up in them or get too long for them. So anywhere from 5 to 9 months.
Cots around 2-3 years old then I would go straight to a bed. Weigh the pros and cons of getting the cots that convert to toddler sleepers. Are they more expensive compared to just going from a cot to a bed? Is it worth it for an extra 12-18 months use? Bed rails may or may not be useful.
Measure your doorways so you know what size stairgate you need and look up prices.
If using formula you go through on average 1-1.5 tins of 900g powder a week. Bottles you'd probably need around 20 for the duration of bottle feeding (not all at once start of having 6-7 in use through the day and replace as they wear out)
There are many types of sterilisers from cold water and milton to microwave steam sterilisers to ones which produce steam themselves.
If breast feeding factor in the cost of breast care items like pads and lotions. Also factor in a breast pump if you want to express and the relative items needed for breast milk storage.
Weaning you only need a few bowls and start with one meal and introduce another when ready. You can puree a portion of your own meals or buy them. The price range is quite wide.
Clothes can be bought from second hand shops, online or from supermarkets. The early stuff of vests and baby grows don't usually cost that much and can usually be bought in multipacks so get researching that now.
Nappies a rough guide is around 6-12 per day (the higher number for smaller babies which are renowned poop machines).
Toys increase in price as they get older and also decrease in size. Look at an xbox compared to a toy car 
The only other big expense is going to be child care and even if you've got that covered research it should your circumstances change.
School uniforms are usually pretty cheap until secondary school with the largest expenses being coats and shoes. There are some areas which recycle uniforms and they are also popular on local selling and free sites. You don't have to have enough uniform for a clean one every day, you can follow a one set on, one set clean and one set in the wash rota.
Buy cheap underwear for potty training as there will be some accidents you just can't face trying to wash out.
Maternity wear, don't bother really just get elasticated and buy a couple of sizes up. Bump bands may be useful though for a bit of extra support.
For the post natal period again cheap underwear and the highest absorbency towels you can find.
Best wishes.