If you are working with a tight budget or a small space, here is the true minimum: a safe sleep space (a Pack 'n Play with the bassinet attachment works as both a bassinet and a crib), a car seat, diapers and wipes, 6-8 zip-up sleepers, feeding supplies, a pack of swaddles, and a sound machine. That is it. Everything else is a convenience.
Babies do not need their own room. They do not need a dedicated nursery. The AAP recommends room-sharing for the first 6-12 months. A bassinet next to your bed, a small changing station (even a changing pad on the floor works), and a basket of diapers and wipes covers the core needs.
For families setting up a full nursery, coordinate this list with your nursery checklist to avoid buying duplicates. And start childproofing before baby becomes mobile — it is much easier to do proactively than reactively.