OP, it's a long time since mine were babies, and I've deliberately not RTFT as I don't want to be influenced.
The things we used to death 20 years ago were:
Muslins (big ones - to swaddle them)
Bibs, as one had severe reflux and refluxy babies get through a lot of bibs
Plain white babygros (though it's now difficult to tell which child is which in any photo of them in a white babygro)
Nappies. We bought loads of washables for DC1 because I am very eco friendly, and ended up using disposables.
Dummies, just in case. I was soooo opposed to them. But we used them with at least one child.
Bottles. Ditto.
Steriliser.
Changing mat (cheap)
Pram which also flaps backwards into a lying position for a young baby. We had a Silver Cross one which did this.
Car seat.
Carry cot.
Baby monitor.
Books. We have thousands anyway, but no baby is too young to be read to. We had a little collection of books which we read from birth. Obviously babies don't understand what's what, but they certainly take in the warmth and cuddliness and rhythm of parents' voices while they are reading.
Music. I had a lovely mobile when they were little (which was when 'mobile' meant 'thing that hangs from the ceiling', rather than 'telephone'). DC1 was mesmerised by it.
I really, honestly, can't say that anything else was really necessary. We didn't have a nursery or anything - we just muddled along. We had them in the same room as us in the Silver Cross carry cot when they were newborn, but not in our bed (not least as I used to wake up in a panic, thinking they had suffocated in bed with me, and I had to be sure that this couldn't happen). One of them slept in the bath next door as she snored so loudly that we couldn't have her in the same room as us. Believe me, we could still hear her. We used to bath them in the kitchen sink when they were very little. Once they were bigger, we put them in the bath, but then had bath seats (which are brilliant!) for the littler ones as I didn't have enough hands to stop everyone from slipping around.