Keeping them in that sterilite with holes in the side will just ensure that they will chew out while you are asleep and chew holes in your socks(or just escape).

I would get another sterilite container and drill just one hole big enough for the water bottle spigot to fit through. Then, using a box cutter(if the lid is thin enough), cut out the majority of the middle of the lid, leaving just the rim to secure it to the tub itself, and replace that with wire mesh. You can either use a staple gun to secure it or use nylon cable ties(Make good use of that Dremel).

Don't worry about the water bottle. The spring-balled ones are the best as they don't leak. Maybe push the ball a few times to make sure it isn't stuck. Sometimes the inside pressure is a little much and won't allow the ball to be moved by teensie meeces.

The lab blocks are a good diet for mice. You can give them a little dog food for extra protein, they do well on it. If you want to give them a treat every now and then, cut an apple into quarters and drop it in. Makes for healthy meeces.