For food,
@Matthew Paz has good advice - try to get the same diet as they were eating at their former home. You can switch over to another brand of pellets, but it's best to do it gradually, since rabbits harbor a community of microorganisms in their gut that is basically tailored to digest the particular food they eat. The microorganisms will adjust to a new diet, but it takes time, and if you change suddenly the rabbit can end up with a major belly ache (or worse).
If you are feeding a good-quality brand of rabbit pellets, that's all they technically need. Many of us also give hay and greens as well, but whatever you do, do it slowly. It's also a good idea to avoid sugary foods (e.g. lots of carrots or apples); while a little bit doesn't generally hurt, too much can cause overgrowth of less-desirable microorganisms and again, a belly ache (a lot like humans!)
Rabbits also need something to chew on to keep their teeth healthy. Pellets can fulfill this need as well, but I like to give our rabbits branches (willow, birch, aspen, spruce, tamarack, apple, etc.) which not only gives the rabbits something to chew and play with, but the bark contains additional nutrients and other healthy compounds. Willow is especially useful as its bark contains a natural analgesic which rabbits will often use to self-medicate. Anyway, your rabbits will likely chew their cages unless you give them something else to work on (and they may
still chew the cages as well!).
As far as nest box bottoms, I use both solid wood bottoms and boxes with screen bottoms. I do actually prefer the wire bottoms as the boxes don't get soaked by the bunnies' urine, and I use them year-round here in Alaska without issue. The perforated material suggested by
@eco2pia looks great and more sturdy than the fine wire mesh I have in my boxes - when I rebuild my boxes I may have to look into getting some of that. My does and bunnies seem to move around in the boxes a lot so I use the mesh for the whole bottom, not just the back.
It's not really necessary and it's a bit harder to build (I build wood next boxes and the lip is about 1" - 1-1/2" wide), but I do like the lip for two reasons. One is that it seems to help keep the kits from hanging onto the mother as she leaves the box - it kind of scrapes them off as she leaves, thus preventing kits laying on the wire and getting chilled to death. The other reason is that it seems to function as a sort of landing platform for them to get back into the box if they do pop out.