I have cats for the moment, and an issue regarding cat litter: even the stuff marked 'unscented' has enough scent in it that it's a migraine trigger for me (and then 24+ hours in bed, meds, the works... ) When I was in the city, what I found worked best for both the cats and my migraines was a brand called Swheat Scoop - basically cracked wheat, kinda-clumpy, absolutely no scent at all. You do need to scoop every day because there's nothing hiding odors, but, given my limitations, it worked (even if it was pricy).
Moved to the country and discovered THE FEED STORE.
A bale of shavings for the bottom of horse stalls is less than 5$, lasts a month if you empty/replace completely every 2 days instead of scooping, and is compostable. More high-tech: cracked wheat (same as I used to use) is 12$/50lbs, and that lasts 2 months for us.
Cheap, completely unscented, completely natural, zero clay, compostable... DONE.
(Trick might not work for city-dwellers, but anyone in the suburbs should be within driving distance of a feed store... maybe google-ing it and swinging by when you've got a car and are in the area might be worth it!)