There's a lot of stuff to think about but financially the big costs for kids are caring for them and requiring more stuff. Caring for them either means one parent stays home and you're looking at lost income, or you pay someone else to watch your kids for you. My wife and I wanted to have multiple children and we planned before we even got married that she would stay at home with them and we would homeschool so there was never really any lost income to think about or costs for daycare. Daycare can be quite expensive from what I've read and in some cases if one spouse isn't making much then their entire paycheck can basically go to daycare which obviously doesn't make a lot of sense. You would get some tax benefit as there's a childcare tax credit equal to 20% of the cost up to a maximum of $3,000.
In addition to necessary items like food (free if you're breastfeeding and still relatively cheap once they tart weaning), clothing, and some minimum baby equipment (car seat, high chair, swing or seat, crib, etc.) diapers are a big ongoing expense. At one point I built a very detailed spreadsheet comparing prices by size, brand, etc. but for years we've just bought the large boxes at Costco along with their wipes. We did cloth diapers with some of our kids for a few years but it's a big upfront cost and a lot of time/effort for not a huge savings. Of course, with three in diapers at one point it was a lot more effort than just one would be.
With one child you can probably get by with your current vehicle and current housing situation, at least in the short-term. A studio apartment with a newborn would probably still work but would be a lot harder with a 3-year old. This is where the costs can really add up if you went from a studio or 1-bedroom apartment to a 2-bedroom apartment. As kids get older the expenses for other things will go up as well. You can save a lot if you buy some things used and if you have friends or family that had a baby a year or two before you they may just give you piles of clothes, bibs, equipment, toys, etc. A co-worker recently had his first child and he said friends of his would drop off piles of baby items at his doorstep.
On the plus side you will get some tax savings. Child tax credit is currently $1,000 (fully refundable) and if you make less than $45k you're eligible for the earned income tax credit which can be a few thousand dollars for one child. You'll also get another personal exemption of $4,050 so if you're married filing jointly with the standard deduction the first $24,850 in income is basically tax free.