Hello & welcome picksgirl!
My bunnies have carpet as their flooring – I find it easy to vacuum up any loose furs off of carpet, and if you use the kind of carpet that they make carpet squares out of, its really easy to use some vinegar to clean up accidental pee spots. My bunny’s cages do not have lids – though occasionally I have come home to a bunny scampering about my apartment because he or she has decided to hop out! I think as long as the cage around the bunny is at least 2-3′ high the bun will not be able to get out.
Where are you going to get your bunny from? I would definitely recommend a rescue bunny because the rescue will help you pick out a bunny with the temperament that you prefer, and also, they will be able to give you a bunny that has already been fixed which is a lot of help both behavior-wise, and financially. Also, a rescue provides a knowledgeable network you can have whenever you have questions about your bunny.