We didn't have twins but we do have 3 boys, so in my experience, Less is more, really!
If you are registering somewhere be sure it's at a place with an excellent return policy, (not Target) Because you might still get 2 or 3 of things and need to return them, then you can pool the money for carseats or something else no one wants to buy you but you still need.
Mention to your families that you would really appreciate them pooling their money to get you carseats, a very needed item, and expensive, please do your research on these and don't buy them because they have a cute print.
Get a nice, not necessarily expensive side by side stroller, that pushes really easily, it does everyone good to get out and get some fresh air, and having a way to easily do that is key!!
Check around and get a carrier so you can wear one baby at a time, check out the Moby, or Katan, should be able to pick them up used, after they are a bit older, check out the Ergo, it is such a great carrier, it doesn't hurt my back, it easily and quickly adjusts so that my DH or I can pop it on, and all of our kids enjoyed it, please don't be fooled by the Baby Bjorn that everyone seems so hot on, those things are expensive crap, and not good for the baby to be held that way.
We never owned a swing,, or bouncy seat, or lots and lots of other baby paraphernalia, We had a small house at the time and I didn't want it all cluttering up my living room, we did borrow a few things to see if our kids liked them and they didn't even care for a swing, so I am glad we didn't buy one.
We used cloth diapers, and they can save quite a bit of money, check out BumGenus Flip system, and just put a tri folded prefold in there for the absorbant layer, they work great and they are one size so they will grow with them, they should start fitting them well around 10ish pounds depending on their shape. I used to teach cloth diapering classes, feel free to PM me any questions you may have, I personally would use sposies for the first few months.
I would just not buy things unless you really find that you need them, their are plenty of 24 hour places open :)
Congrats on your twins!