We were adopted by a stray cat last year, and boy does she have us wrapped around her little paw!
I clean the litter box(es, actually) every day...sometimes multiple times a day. My thought is that I wouldn't want to have to dig around in my previous "business" the next time I used the bathroom, so why should she! Honestly, it takes less than a minute, why not?
We don't have to dump and wash the litter box as often this way either. I do that every month when I give her her Revolution (heartworm, flea, tick, etc.) medication.
We use the Arm & Hammer Multicat formula (available in scented and unscented) even though we only have one cat. We have no problems with odors, and we live in a one bedroom apartment, so it is close quarters.
Also, most cat care websites and veterinarians recommend having one litter box for each cat, plus one. For example, if you have two cats, you would have three litter boxes.
I cat-sit for a neighbor occasionally. She has three cats and one litter box. Scooping twice a day isn't even enough at her house! P-U!!!
Better safe than sorry! Plus, with a kitten, you don't want to have them too far from a litter box when they realize they have to go! Cat pee stinks, and you can never get the smell completely out unless you can thoroughly soak the item in a disinfectant and put it in the washing machine.
Just my two cents. Every cat is different. Hope you enjoy your new little one!