I'm a SAHM, and we CD, BF, and co-sleep. We are also fortunate to have a loving extended family that has the means and the interest to buy what we ask for as gifts.
For our first baby we spent about $800 on the stuff he needed for his first year. That went to:
About $200 on cloth diapers (we use flats and wool covers), and an additional $50ish on laundry.
About $100 on a fancy, preemie-approved infant car seat (he was a 28 weeker).
About $100 on clothes and accessories (most were used or homemade).
About $50 on a convertible carseat for when he outgrew the infant seat (most kids outgrow the infant seat within the first year, so I would recommend just using a convertible right from the beginning unless you have special circumstances like we did)
About $100 on supplies to make baby carriers (a woven wrap and a mei tai)
About $50 on toys (again, used/homemade will save you a lot of money)
About $50 on miscellaneous gear (used high chair, used bouncer) that we could have done without but I liked to have
About $50 on traditional needs (first Christmas ornament/stocking, etc.)
And about $50 on maternity clothes and supplies for making my own
Then there's the stuff that's hard to calculate, like buying extra food to support pregnancy and lactation, heating the house a bit more (especially important if you have a homebirth), increased rent/moving costs if you need a bigger home, and increases in your insurance premiums.
There are other incidental costs as well, especially if you are surprised by having a medically fragile kid, like medical care, gas for traveling to/from specialist appointments and NICUs, eating out more, lactation consultant appointments and hospital-grade pump rental, milk storage supplies, prescription co-pays, preemie/micro-preemie clothing, home medical equipment rental, etc. But we were able to cover those with LO's SSI.
But I would say that in general, if you don't pay for childcare, formula, baby food, cribs/playpens and other containers, baby electronics, or disposable diapers, you should budget $1000-$2000 for a first child's first year depending on COL in your area. Subsequent babies are obviously much cheaper, representing only a few hundred dollars outlay, as you only (generally) have to buy a new carseat and a few new items for seasonality or to replace things that have worn out.
Many people, instead of saving up to have a baby, buy clothes and gear and diapers incrementally over the course of a few years before they start TTC. But if you go that route, you might end up wasting money buying things you THINK you will need/like and then discovering, once you have the baby, that you are not the kind of parent you thought you'd be. For example, I bought a bunch of footed sleepers and bodysuits in the years leading up to the birth of my first child, but it turns out that we have string bean babies and are better served by gowns and separate tops and bottoms.