Unsolicited advice time!

Just remember: you can get lots of dumb crap for your kids, but you do not need most of it.

Car seat, yes. Somewhere safe for them to sleep, yes. We had a changing pad on a dresser with the first one for a while, but switched to the floor pretty quickly and didn't bother with it at all for the second. You're usually not gonna want to take the kid to wherever the changing pad/table is, and it's easier to dress them on the floor anyway. And you don't have to worry about them falling off of the floor. My conclusion: changing table/pad = junk, unless you have some kind of problem getting down to/up off of the floor.

Bottle warmers. Waste of space and money. Also slow. Just nuke it. Shake it and stick your finger in to make sure you haven't done something horrible. It won't take long (a day) to figure out the right amount of time, at which point you'll almost never mess up anyway.

Favor 8oz bottles, not 4oz. They'll outgrow 4oz ones too fast and then they're basically garbage. Buy ONE BRAND AND STYLE ONLY so the parts are interchangeable. Do the same with sippy cups when those become relevant.

This part's (apparently) controversial, but: you don't need a giant diaper bag and a huge amount of storage on your stroller. When you go out you need: 1-2 diapers, 3 tops, a little plastic bag with wet wipes in it, one bottle, stuff to go in the bottle (this is easier if that's formula, you can acquire warm water one way or another almost anywhere so you just need the pre-measured powder in a baggie). THAT IS IT. You don't need crackers and fruit snacks and a dozen toys and that junk for your toddler. Just don't give them food when you're out shopping or whatever. Real easy if you don't set the expectation that they get snacks and toys all the time when you're out of the house, and that's as easy as... not doing it. So you don't need to carry that crap. You don't need a backpack. You don't need a massive $200 baby bag that you could fit 10 of your baby in and still zip it up. You don't need a stroller that could double as a truck. If you're getting a stroller optimize for ease of maneuvering in crowds (so, small), comfort to push (not too short if you're tall, for example) and ease of transport (collapsible). With one kid especially, consider just getting one of those strap-on carriers and skipping the stroller entirely. When they start to walk, make them walk whenever possible to reduce the amount of time you're dependent on that stuff.

You can buy giant loads of kids clothes off Craigslist or that Facebook Swap-Shop thing (I dunno much about it, my wife uses it, I don't have an FB account, but it seems to work well). It's even cheaper than the thrift store. You can buy for next year at the end of each season, works well. Then you sell anything that's not ruined when they grow out of it (or hand it down to a sibling). Clothes end up being nearly free unless you choose to spend more for some reason. Protip: hold out for batches of clothes from nice parts of town and then pounce on them immediately, the clothes will be in much better shape (sometimes brand new) than stuff from poorer areas and usually aren't more expensive(!). Difficulty: you will have to buy new shoes, usually. Just get the cheapest thing that works, they'll ruin/outgrow them quickly anyway.

If you have older relatives and they're not destitute, you'll soon be donating or throwing out excess toys and books by the bin-load. Buy way fewer toys than you think you "need" if this is your situation.

Remember you can always go get more stuff if you decide you need it. Err on the side of starting with too little in general, once the basics are covered. Keep most of the baby shower stuff you don't obviously need in the packaging until you decide you need it, and keep the gift receipt. You may never open it.