I stopped using the clumping clay litter about 6 years ago and I'm so glad I did. I have three litter boxes for my two cats, and they're all the
Purina Breeze boxes. We use the breeze pellets and pads in the two upstairs boxes (the ones my younger cat typically uses), and Feline Pine pellets in the downstairs box that Bandit typically uses. The Breeze pellets are completely dust free and awesome. The bottom of the box is slotted, and the pee gets absorbed by the pad in the tray. You change the pad once a week (per cat) and the pellets once a month. The one caveat is that it's not so good for runny poop, which is why we keep Feline Pine around for the other box (Bandit is on immunosuppressants and will sometimes catch a stomach bug and has what I call "Kitty Poop Explosion Disease").
We still use the slotted Breeze tray with the
Feline pine (non clumping), but we don't put the pad in the tray. When the cat pees in the pine litter, it turns to sawdust, and you sift it down into the tray through the slots. When the tray is full (typically every other day or so at my house), I dump the sawdust out. With the Pine, you don't have to change out the pellets once a month like you do with the breeze pellets, you just add more in the box as needed. You are dealing with sawdust, but it is nothing like the clay dust that's in clumping litter--it's heavy and falls right to the bottom of the box, so it doesn't get inhaled or leave residue on anything like the clay does. You can also use the Feline Pine in a regular litter box, but I prefer the slotted box because you can keep cycling through your pellets for less waste, the box stays cleaner, and is easier to clean, in my opinion. I think Feline Pine makes a slotted tray type litter box for their litter also that you can buy (I already have the breeze boxes which is why I use those). There are other brands of pine litter out there, but in my experience Feline Pine is by far the best for odor control. Our boxes are right out in the open (one in the dining room, one in our only bathroom, one in the bedroom), so it's very important to us that they are always clean and don't smell at all, and don't track dust all over our house.
As for poop, with both boxes you just scoop and either flush it or dispose of it in something like a Litter Genie (our pipes are sensitive in our new place so we've used a Litter Genie since we moved).