It’s very different having twins after a singleton, vs having twins first.  You have a toddler to deal with, which necessitates different activities.  More relevant to this discussion, though, is that you already have some things and you’ve developed preferences for what you actually use.

Here goes on the double question (after a singleton). Some of this will depend on your preferences.

I need 2 of: car seat, crib, pack n play, high chair, bouncy seat.  Most of these are safety issues so they can’t really be debated.  I think most people would like a second bouncy seat, vs other locations for infants, but there is some personal preference here.

Need more of, but not double: bibs, crib sheets (I went from 4 total to 6 total), bottles (personally I like to only have to wash once per day, but that’s up to you)

Nice to have with twins that I didn’t have with one: swing (one is enough as your child might not like it anyway but they’re great when there’s one adult and they’re both crying), two bumbos.  Not everybody likes the bumbos, but I found them invaluable for storytime with three.  I could set them up in front of me like you see at library storytime vs trying to cram them all on my lap.  That never worked very well.

Things you likely have that you don’t need more of: activity mat, exersaucer/jumper, changing pad covers (assuming you have more than 2 already), carrier so you can carry one and put the other in the stroller/shopping cart/etc (unless both adults are willing to carry).

You’ll also need a double stroller, or triple if your kids are too close together.  I’d vote for the double if at all possible.  If necessary you can put one twin and the older one in the stroller and carry the twin.  The older one will learn to walk soon enough and triple strollers are even more expensive and bulky than doubles.

My oldest turned two right when our twins were born. My super practical recommendation is to think about where you go by yourself and how you will navigate those places with three kids. Fundamentally, there will be places that go off your list until the twins can walk.

It is key to determine who does, and does not have automatic doors. You’ll be amazed at all the doors that are a complete pain in the ass with a double stroller that weren’t so bad with a single. You basically have to wait for someone rather than wiggle yourself and the stroller through a manual door.

Second, think about places that your oldest likes that you can manage with two buckets and no stroller. Yes, you get even more stares than with a double stroller! But, I found it doable to carry one bucket in each hand pretty much until they outgrew them; you’re actually better balanced than with one. So, places like McDonald’s where you can park right near a door and then just plunk everyone down at a table make for good outings. The grocery store is also manageable if you can put your oldest in the plastic car, one bucket on top, and the second baby in a bucket in the basket or a carrier. My oldest liked being in charge of the canned goods and other stuff he could stash in the car without worry.

Finally, get to know the drivethroughs. I’m not talking about fast food here, but banks and other errands that don’t require getting the kids out of the car. It helps to have a stash of these types of errands in the car for when they all fall asleep. I kept a crossword or such for myself also in case I ended up just parked someplace.

The oldest may or may not be helpful with the twins.  The twins will learn to walk at some point.  At some later point they will learn to walk together; this is your big goal and will really enable you to go places you’ve left off your list for years.