The corner litterboxes are too small. I know it seems like there is enough room... but it isn't sufficient, even if you have perhaps a Netherland Dwarf.
You mentioned you have a cage. Does it have a plastic bottom? And is it the largest cage available? I realize that most people here either have House Rabbits or bunnies they let out for more than a few of hours a day to roam in a designated area in the house. Please understand that a rabbit, regardless of size, will never be able to get the exercise it needs in a cage and it needs more than a few hours to get it's exercise. I would highly recommend that when you've got the cash, to get rid of the cage and actually get a metal puppy play pen. They are often made my Midwest or Prestige. If you are worried about accidents, a cheap roll of vinyl flooring used as a base for the play pen rocks. This is how many rescues house the rabbits they bring in. You will like, any way, cleaning when bunny is in a play pen... it is easier and quicker than trying to empty a cage. And bunny will be able to get more exercise this way. I would recommend the dimensions no smaller than 4 x 4. Depending on breed (or jumping ability) 30" up to 42" in height.
If it is a young bunny, especially if still a baby... exercise is very very important. The lungs are developing and a baby needs to move move, otherwise it is at a bigger risk to illness.
And rabbits usually drink more water when it is in a large heavy stoneware dog bowl. Bottles are not the easiest to keep clean, they can store bacteria (rabbits get bacterial infections)... and the ball can get stuck or clogs... the metal ones without the ball are a magnet for calcium build up and do clog, I've also heard of some rabbits getting absesses on their tongue from the rubbing on the metal stick to release the water lick by lick.