These questions will probably differ to the type of cage you get for your rabbit. Are you looking at a wire-floor, wood floor, or a plastic floor?
From your first question about the drop pans, I'm assuming your thinking about a wire floor. With my drop pans, I put a layer of kiln dried shavings in the bottom - although I may be adding a layer of newspaper over the top, that way I can betterly seperate the urine in the shavings, from the pooh which goes straight to a bucket for manure/fertilizer. In litter boxes, you might use the same thing you use in the drop pans, or you might use wood pellets (I actually prefer wood pellets in my litter boxes, but at this time, I have none, so I am using shavings.)
On the floor of my wire cages, I use EZ Mats, which can be purchased at your local farm store, or via online rabbitry suppliers like Bass Equipment, KW Cages, and several others. You can also place a chunk of wood in the cage that takes up maybe 1/3 of the floorspace. That way, pooh and urine will still go into the drop pan, but your rabbit will have a place to get off the wire.
I don't feed veggies very often. My rabbits get them about once or so a month, and it's more of a treat, not a necessity in their diet. But, I have 10+ rabbits, and purchasing enough veggies to feed them all would be costly, and that's why I don't feed them veggies that often. They do get grass almost weekly, as well as dandelions and dandelion greens. So they do have some greens in their diets, just not a lot and not all too often.
Emily