Since I use my compost to supplement my soil rather than for gardening, I compost kitty litter. It's convenient for me to do that, largely because it's inconvenient for me to haul it to the transfer station and because it seems like a waste. Cat crap will compost, after all. I wouldn't feel as comfortable using it in compost that I was going to garden with. I doubt that it would do any harm, given that my compost sits for at least two years. But still. Given this, I use mostly compostable kitty litter. I do occasionally use some clay-based litter because clay, after all, is a natural part of the soil. But too much of it makes a mess. I have used kitty litter made up of crushed walnut shells, corn-based, wheat-based, pine-based, and paper-based litter, although my cats don't like the paper stuff or the pine. I don't much like the paper-based stuff either because it's not scoopable. Although Amazon doesn't carry it anymore, I am using some hemp-based kitty litter that I like quite a lot, and the cats like it too. It's not scoopable but it was really cheap. Overall, I think the walnut-based stuff works the best. It's very scoopable, lasts a long time, and the cats seem to like it. With two litter boxes filled with walnut-based litter and one with the hemp-based stuff, that was ideal. If I can find the hemp-based litter yet, I think I'll stick with that for a while. The cats would urinate in the hemp-based litter and crap in the walnut-based litter. When it comes to the use of litter boxes, it's always good to keep the cats happy. The corn-based stuff that I used (Word's Best) works as good as the walnut-based stuff, but it's awfully expensive.
It's been years since I've had critters. I had no idea there was such a range of kitty litter materials. I recently saw a commercial for disposable litter boxes. I believe it's a subscription (automatic delivery) service. You receive a new collapsed box with fresh litter in it, and you just fold the dirty one up and I believe it goes out with the trash. I don't think there's a recyclable component to it...and you certainly could not ship it. Litter boxes are absolutely the worse part of having a cat. If I had a cat today I'd pay for someone to make this aspect convenient and painless.
There isn't much of an odor, though, if you use the scoopable litter, and empty them at least once a day. The problems were a lot worse when the traditional clay litters were the only option.