We put them in moses baskets till about 8 weeks then both in one cot bed in our room till 6 months. Even if they are happy in the cot straight away the baskets will be handy for daytime/living room. Probably 4-6 sheets & 4-6 cellular blankets. Nice to have but not essential - rocking stands for the baskets. Def another bouncy chair.
Changing mat, nappies, nappy bags, water wipes, cotton wool, muslins (about a million). A big, easy to carry bag for all of this and a couple of spare sets of clothes when going out - a rucksack is just as good as any special changing bag. A little fold up changing mat is useful.
Number of clothes depends on whether you have a tumble dryer! get a tumble dryer I think we got though at least 3 sets a day. We didn't really bother with anything more complicated than a vest & babygrow until about 4/5 months. Get the babygrows with the built in scratch mitts, separate mitts just refuse to stay on. You might need a couple of pairs of little socks/booties, cardigans if it's a cold time of year. Sun hats if summer.
The first few weeks are all about the feeding. For breastfeeding a tandem cushion and Lansinoh nipple cream, but tbh knowing where to get good twin bf advice and support is more valuable than any bit of kit. You don't have to buy all the bottle feeding kit too, but it's at least worth knowing what you want and where to get it from quickly as you are more likely to need to express or mix feed (steriliser, pump, about 6-8 bottles). We hired a good hospital grade pump from a private bf consultant, which was great, but I think some maternity units have ones they will lend out for free.
Other things that may be essential to some but not everyone needs - baby monitor, sling/wrap, swaddling cloth, dummies, baby bath/bath support seats. Things that I've never seen the point of - top and tail bowl, nappy bin with special liners, heated wipe holder(?!).