The best toilet paper for backpacking is a paper towel. Regular toilet paper just doesn’t stand up to the humidity.
I like using Brawny paper towels: they’re scored down the middle of each sheet, so it’s easy to tear off a half sheet. When I pack my toiletry kit for a trip, I tear off 5 half sheets for each day of my trip. Then I tear these in half again, producing 10 quarter sheets for each day. I pack these in ziploc bags, along with one Wet Ones antibacterial wipe for each day I’ll be out. They come individually wrapped. Make sure you get the unscented kind to avoid attracting bears.
I bring the Wet Ones along for two functions. They contain Aloe which can be soothing when necessary and a moist wipe can help ensure that your butt crack is clean. This should be obvious, but monkey butt (diaper rash) can become very painful if you are hiking long distances over multiple days. The best cure is prevention and if that fails, zinc oxide.
Paper towels are biodegradable. But I don’t always bury them in a cat hole when I’m hiking or drop them in a privy. It really depends where I am and what the terrain is like. Sometimes, I’ll pack out my used towels and waste in a wag bag, so called, after the bags people use to hike out pet feces when they hike with their dogs. I always carry out the used Wet Ones. You don’t want to drop them down a privy.
I got over the embarrassment of talking about backpacking hygiene years ago. If this is all new to you, I strongly suggest you buy How to Shit in the Woods: An Environmentally Sound Approach to a Lost Art which explains in great detail how to properly minimize the environmental impact your waste has on the environment. It’s a backpacking classic, but also a fun read. It also makes a great gift if you’ve got someone in the family who is just getting into backpacking.
Disclosure: The author owns this product and purchased it using their own funds.