For new parents, how did children affect your budget?
I have two boys; one is 5 years old, the other is 5 months old.
The oldest cost about $1K in terms of pre-natal, delivery, and post-natal care. The youngest cost about $4K, but the difference was mostly a function of the different healthcare plans I had with different employers at the time they were born.
The cost of food is negligible at this point. That will change when they hit adolescence. When they're very young, your wife can be their primary source of nutrients. The cost of formula is a different story, and I don't know how much formula costs. Studies have shown that breast-feeding enhances both the child's immune system and his intellect. We're strong advocates of breast feeding.
Depending upon the size of your and your wife's extended families, you'll be showered with baby clothes (pun intended). If you have more than one child, you'll have both the hand-me-downs from the first child and new clothes for the second. It helps to have children who are all the same gender, but at such a very young age the gender doesn't matter. A baby is a baby. If you have two boys or two girls, you'll have too much clothing for the youngest by the time he or she is a year old. Children grow so quickly that consignment shops, Ebay, Craigslist, and even Goodwill are swamped with high-quality, clean children's clothing. Let the grandparents indulge them with new clothes, but get most of their clothing from those other sources. Again, this will change by the time they hit adolescence. I think having boys is cheaper than having girls in this regard. (I have many nieces)
Diapers and pullups can be expensive, but you're likely to receive these as gifts as well. I think we spent about $500 total on Boy #1's diapers and pullups through the years. He's wearing X-Men superhero underwear now. We tried modern cloth diapers on Boy #2. So far, it's been no fun. We'll try again when he's about a year old. I won't go into detail, but things change at approx. 1 year old, and cloth diapers are better suited after those changes materialize. Cloth diapers will likely save a few hundred diapers, and they are better for the environment. But don't underestimate the value that disposable diapers add to your happiness.
Toys are like clothes, only more abundant. Children outgrow toys, and you'll find good quality toys everywhere. Try garage sales and Ebay. Aunts, uncles, older cousins, and grand parents will all shower your kids with toys. We have so many toys that we need to smuggle them out of the house when Boy #1 is sleeping to make room for more, and we generally don't spend our own money for toys.
As for schools; this is where it gets expensive. You'll either pay for good private schools, or you'll pay for real estate in a neighborhood with good public schools. We did the latter; in fact we bought a relatively inexpensive house (~$400K) in the best school district in our state. Our house is a mile from the elementary and middle schools, and two miles from the high school. The mean home price in our zip code is more than $600K. It took years to find our house, and we pounced when it hit the market. It went to contract before we could bid, but that contract fell through and we were stunned to learn that we had the house. If you're going with public-schools and need to change school zones, I recommend positioning yourself to pounce on a home early as possible.
Obviously, life with children is more expensive than without. But it doesn't have to be exponentially more expensive. For example: We like to go camping, so we need a bigger tent and more sleeping bags, but we don't need bigger vehicles. The incremental cost of having more than one is low, especially if they're the same gender.
College costs are a different story. We have a 529 in place, but we have no intention of paying all college costs. I expect the landscape of higher education to be very different by the time Boy #1 is 18 (2027). I don't believe that costs can continue to rise at their current pace, and student loan debt cannot continue to grow at its current pace. Rising costs and rising debt only serve to erode the value of a college education. My wife and I both have Master's degrees with no student loan debt, and we both agree that going into debt to obtain those degrees wouldn't be worthwhile.