Kids, at least for the first couple of years, don't really require that much stuff, certainly much less than most people buy. Beyond clothes, bottles and consumables (like diapers), all you really need is a carriage and/or carrying device (I highly recommend getting both) to transport the kid, some sort of crib like thing for the kid to sleep in and some simple toys.
Ask me again in a couple of years time and I'll let you know if you need more stuff for older kids.
And its not just a matter of what you get them. Birthdays, Christmas, random gifts from grandparents and other relatives and friends, and before you know it you can't walk across their bedroom for all the crap that's accumulated.
Good plan is to say "ok now that you have this new thing we need to get rid of one of your old things" but good luck getting them to accept that happily.
One suggestion I'd make (that I haven't seen implemented, so it's only an idea) is a regular cull. Every few months or a year, depending on your preference / tolerance, just sit them down and ask them to choose what they're willing to throw away or give away. You could explain it in terms of your philosophy, or frame it as giving their lovely things to other kids who would also like to play with wonderful toys, or so on.
Kids can be a lot more reasonable than people give them credit for.
Diapers are a great example of balancing minimalism. Cloth diapers are cheaper in the long run and use less space, but they also take more time and energy to maintain than disposables.
Ask me again in a couple of years time and I'll let you know if you need more stuff for older kids.