The role of sawdust/shavings in composting toilets is four-fold:
- Visually hide your waste so the next person using the toilet doesn't need to see it
- Trap gases immediately above the waste so that they don't waft into the room
- Absorb some of the fluids/urine
- Add carbon to the high-nitrogen mix so that the composting process can begin
The labelled 'quality' of the sawdust/shavings is pretty-much irrelevant. 'Premium' doesn't mean anything. Don't pay extra for it. Use the cheapest sawdust/shavings you can find. As long as they come from pure wood (not manufactured products with glue/paint/resins in them), and are dry, you'll be fine.
Perhaps the most important characteristic of the sawdust/shavings is how easily they can be scattered. You want to quickly apply a layer over everything without having to think too much about the process or spend a lot of time doing it. If the sawdust/shavings tend to clump rather than scatter, then you may want to consider a different source/type.
Note that many commercial products are compressed, so if you are using them straight from their original bag, they will tend to clump. This can be most easily solved by using an intermediate pail/bucket/tin. When you transfer the sawdust/shavings from the bag to the pail/bucket/tin clumps have an opportunity to break up. When you then actually use it clumps have a second chance to break up. Loose/fluffy cover is good cover.
As for the amount you should be using, keep in mind that you want a 30:1 C:N ratio in a regular compost pile for the bacteria to be happy. That translates to a lot more sawdust/shavings than people think. When you're paying for the cover material, there is financial pressure to minimise the amount you use. Many folks tend to apply less than they should.
A fresh container should have about 6-10cm of sawdust/shavings placed in the bottom before it is even used. Most of your urine/liquid waste will make its way to the bottom of the container, so you need something there to help sop it up. Applying roughly 3cm of cover over fresh waste should be adequate. Not being able to see any waste — except for the odd corner of toilet paper — is a good guide.
The biggest challenge with composting toilets is the water content. People drinking a lot of water tend to generate a lot of dilute urine. Purchased sawdust/shavings makes for an expensive sponge. Depending on your domestic arrangements and conditions, having males (and females that are able) urinate somewhere else relieves a huge burden from the compositing toilet. If you can have a separate toilet/urinal just for urine, that's one way to solve the problem. If you have fruit trees out back that can do with direct fertilising, that's an even better way. Excessive amounts of fluid in the container is the most common way to saturate the mix and turn it into a stinky, anaerobic mess.
If you can reduce the amount of fluids going into the container, you can get away with using less (sometimes a lot less) sawdust/shavings. This means your container needs to be swapped-out/emptied less frequently and (if you purchase your cover material) you save money as well.
We use sawdust that comes from processing our own firewood with chainsaws, and from woodworking projects in the shed. Sawdust is collected and stored (suspended off the ground) in highly porous bags for at least one summer. It's then ready to use inside. Since our sawdust is a by-product (essentially 'free'), and I produce far more than we need, we apply cover material liberally and don't have odour issues.