Some random thoughts, in no particular order, having had 2 children but not twins.
I would get two baby-holding devices, maybe one swing and one bouncy. Or the rock n play, people love those.
I would start with one or two pack-n-plays, two if you can get them used- but I wouldn't shell out for new. That way you have the flexibility to put them down separately if needed (or if one hurls all over..... )
For a rocking chair, I loved mine. We got a regular old recliner, actually. Comfortable for nursing. I found hard wooden rocking chairs horribly uncomfortable, you want it to be fully padded. OTOH any comfortable chair will do. With twins, I would want a chair wide enough to fit the giant twin nursing pillows so you can do both babies at once.
Speaking of, I would buy a giant twin nursing pillow. Then, i would buy a second if nursing works out for you, as I expect you will want them in a couple different locations in the house.
I would have a breast pump on hand even if you are dead set on nursing. I nursed both mine, but used the pump fairly early on to help relieve engorgement and pump a little extra milk for the freezer.
Definitely a double stroller and 2 car seats, as mentioned. Look into which brands of baby buckets have lower weight limits and get those in case you have tiny wee babies. We flying, my kids have been both lap babies and in car seats, and they slept much better on the flights in their car seats. If under 2, i could still nurse even during take-off, but then i could set them down after nursing.
For cloth diapers, if you plan to hang to dry you will need quite a few extras as they take a while to dry. Plus there are the days when they pee and poop every 15 minutes. I would get 36-48, but not all fancy types. Plain flats and prefolds are cheap and good for when the fancier ones are hanging to dry.
For bottles, I found having 2 per baby was enough. One to be used if I left them, and one extra in case of emergency. Obviously if you are going to work you would need more.
Honestly you don't even need baby shampoo. Just rinse them off. The worst they will smell is curdled milk, and water will get it off. You might get some plain non-allergenic lotion though, as many babies are born with dry peeling skin.