I have had house rabbits for about 20 years, and we've got two house rabbits that live in a small room in our house currently. Both use a litter box with occasional pellets droppings outside of the box, which are super easy to clean up. That room is bunny-proofed against anything harmful that they could chew on, because bunnies do chew! We did rip out the carpet in that room and replaced with a sheet of vinyl flooring, for easy cleaning and sometimes rabbits will chew on carpet which is really bad for them. I put little throw rugs in for them, which I can clean easy (and easily remove if the chew on them). The fine fur is really the thing that I find harder to clean, but I use a cordless Bissell pet hair eraser hand vacuum, which is really handy! I also gave them plenty of wood and other things to chew on, and even built them a little castle out of untreated wood that they like to sleep in (and also chew).
The large closet you are proposing sounds like a great idea and size. If you get rescue bunnies that come spay or neutered (we did that), they have better litter manners. It can be challenging sometimes to bond rabbits. But if you go to a rescue sometimes you can adopt two that are already bonded also! I have had many house rabbits, and found that the ones I adopted from a bunny rescue are the best matches for us. The rescue will let you know about the rabbits' temperaments, which can range a lot, they have very distinct personalities and cuddlability. Case in point, we have one that is a complete cuddle bug, and the other is hands off. To second the baby gate issue, mine have chewed through a plastic gate, so just make sure you have one with metal (we have that now, and no issues). Depending on the rabbit, get the tall gate

!
This is a great resource if you haven't seen it already:
https://rabbit.org/ , and if you adopt from a house rabbit rescue, they will give you lots of info. If you were interested, we use Carefresh litter in their litterboxes (Chewy has the best price), Oxbow rabbit pellets, with unlimited hay and fresh water. And of course veggies. The House Rabbit Society has a good write up on appropriate veggies (not all are equal to the buns).
We let them into the rest of the house when we are home, generally they like to explore in the mornings and evenings. We've covered all electrical cords with plastic cord covers I bought at home depot, and used baby-proofing covers for the sockets.
Sorry if it's too much info- we love our bunnies, and hope you love having one (or more) in your life! Best of luck with your new addition!
This is our rescue English lop, Della with her crinkle tube.
View attachment 1982213 She's actually hopping around our living room as I write.