Nursing bras: I would get cheap stretchy ones to start with and enough to have at least three-four changes in 24 hours (spit up, milk leaks, and sweat), with some in the wash. Enough clean bras made me feel better.
Just for balance, I'll add my experience, which is quite different to the above (I'm not saying it's invalid or wrong in any way at all, just saying that everyone is different)!
I wore nursing vests 24/7 during the early days (a change for day and night) and then switched to only wearing them for sleeping (it's nice to have some support during the night, but I don't feel I need the same support as a nursing bra). I wear the same bra all day and just insert fresh pads when required (I used disposable at first, but switched to reusable a couple of weeks in once my supply was a bit more settled and I needed fewer pad changes per day). In your shoes I'd just buy the same number of bras as you'd usually buy on a regular basis for routine wash and wear. I agree that relatively inexpensive and stretchy (definitely really stretchy for the initial bras) is the way to go, you won't be able to predict how engorged you'll get or your 'breastfeeding cup size' (which will probably fluctuate somewhat anyway).
...You'll have lots of people say 'you need this, you need that'; we had friends tell us we needed tons of muslins and bibs, so we stocked up, but the reality is that we only needed a third of the amount that they did because our babies were much less 'sicky'! My point is that nobody can really tell you how much you'll actually need of anything, because your baby, your body and your experience will be different. It's easy to shop for items fast these days, so I'd ensure you have the basics covered and then buy as necessary after that.
Bearing in mind what I said above, I'd suggest the essentials would be:
Hats - 2 (one to wear and one spare/to wash)
Bras - as many as you'd usually buy for routine daily wear (minimum of 2, one to wear and one spare/to wash
Bottles - I'd initially buy 2, if you're planning to breastfeed. If you only use bottles because you're expressing milk, you'll need to sterilise the breast pump regularly and so having one bottle to use and one to sterilise on rotation would work until you figure out what works for you long term. Mam or NUK are good teat shapes for breastfeeding, just make sure you go for the right size and flow for breast milk. With my first child I never got beyond using two bottles on rotation (and then phased them out as I no longer needed or wanted to pump), same goes for my second baby (although I didn't actually touch the breast pump for weeks, until I needed to pop out for a couple of hours on my own!).