Hi there Ticagrumpy, and
to ATP. So glad you found your way here.
The best time to buy and plant new sempervivum is in early spring. That is when they are actively growing after their winter dormancy.
It helps us to know what part of the country/world you live in, so we can consider what your special growing needs might be.
Kitty litter would not be something that would be safe to use in or on the soil. It can compact and also retain to much moisture, this would be harmful to your sempervivum. Instead use small gravel such as chicken grit or small pea gravel.
Here is a photo of what the chicken grit looks like. Just be sure it is not the chicken grit made from oyster shells, but from granite or some other crushed stone.
I hope this was helpful information?