Hooray! I threw the old litterbox that was falling apart and Juni just started using this one (with litter). If you remember, I said before, Juni was using her boxes only with paper or nothing. Now, I just bought some litter, poured it in the litter box and she used it like this was not the almost 2 years old litter box.
I liked the covered ones, but I am not sure if Juni would use it.
About cleaning them, I wash them with bleach or some other washing liquids at least once a week.