I would get muslins or some other type of similar cloth because you can use them for anything for years (we still use our old ones for things and my daughter is 4.5 now). Things you need for feeding and sleeping.
If you plan to BF, I would get some nipple cream and a pump unless you absolutely don't plan to pump ever (it can be really crucial for getting your supply up if you have any trouble early on). If you plan to FF, then bottles, steriliser, bottle brush and something to soak bottles in when cleaning (you probably won't want to use whatever you use for other dishes and pots as the fats can adhere to the bottles and be hard to clean).
Then blankets, sleeping bag, fitted sheets, waterproof mattress cover (there will be leaks) for wherever baby will sleep. Wipes. I would buy a gentle scent free bran you like in bulk if it's cheaper. You'll go through them fast.
A changing mat. I found the one that went across the top of the cot and was movable was the best. During the day, we would bring it downstairs so I could do changes on the floor downstairs without having to run up and down the steps all day.
We didn't really have anything like a bouncer chair until maybe after 4 weeks. It was handy because I needed to pump so I could put her down in that while I was pumping. But we ordered it online and had it delivered when we realised we wanted it. It's not something we needed straight away.
The one thing I am grateful we had before that was really lifesaving from the start was a moby wrap. It helped so much when I just needed my hands free, especially after my husband went back to work. It takes some practice and getting used to, so I was glad we had it before so I could practice a bit before I was too completely exhausted to work it out.
You don't need loads of toys or books at first. Or really any of it. Probably by 3-4 months, they'll have an interest, but they are really too little before that. You also don't need any clothes that aren't vests and sleepsuits. We had a few outfits that were bought for us as gifts, but we never bought any ourselves in the first 3 months and we barely used them. Just very basic clothes will do it until they get a bit bigger.