CONGRATS!! i feel like it was just yesterday that i asked the same question on here! We had boy/girl twins born in December - early and tiny (27 weeks gestation... 1lb 13oz & 2lb 6oz) and were in the hospital NICU for 11 weeks... i'm sure yours won't be THAT early, but just make sure you're prepared for them being at least a little early, twins often are! We were nowhere near prepared but at least had their hospital stay to get things ready!
You already have great responses, but i'll just weigh in...
The only things we NEEDED two of were the carseats and cribs. We only used the basinette when my son came home... when my daughter came home, 10 days later, we went right to sleeping them in the crib (they're still sharing one crib) - so i'd say any basinette/baskets are an extra, not necessity.
Another must for me: a really good breastpump (unless you're planning to exclusively feed formula)... i intended to exclusively nurse, but it didn't quite go as planned. So i pump and they get bottles ofmy milk, and some formula.
other than that we've found it helpful:
*2 Boppy pillows - if only one of us is home, we can sit them each in one and bottle them at the same time, and they like to sit propped in them while we play... not necessary but nice!
* a bouncer & swing to give your arms a break - but not necessarily 2 of each (one of our twins likes the swing, the other prefers the bouncer)
* a pack-n-play (they nap in it together during the day and can use later on as playpen wherever you go - very portable!)
* a double stroller
* a monitor (we just have a basic audio one, i felt the video one was just an uncessisary luxury!)
* "tummy time" mat (or we often just use a nice thick quilt for tummy time)
* 2 Bumbo chairs (our babies are too small to use them yet, but a fellow-twin-mom swears by hers!)
* and evenutally 2 high chairs (we have the compact ones that strap onto a diningroom chair)
And clothes... by far the #1 thing i'd recommend is Halo Swaddlers (the NICU sent us home with 2 and we got a few more!) so much easier than swaddling with a blanket! And our little ones fuss a lot less in them!
* The gowns are nice for night changes - no snaps!
* Lots of onesies and one-piece outfits that are easy to snap open
* And a few cute outfits for outtings!
As far as sizes, even our TINY preemies didn't fit in preemie clothes long, but get plenty of NB, 0-3mth, 3mth, 6mth, etc... it all depends on if you're having boy/girl or same sex twins as to how many you need... we needed almost 2 separate wardrobes (but got more than enough from our shower and from hand-me-downs of other twin and singleton parents we know!)
My biggest philosophy in our twin journey so far is that hand-me-downs are gold! Their nursery is full of nothing but hand-me-down and garage sale finds.
Sorry my answer was so insanely long!!
Good luck!! If you have any other questions i always love to talk twins!