The most critical thing about a run is location. If you put it where water drains to it or water stands in it you goofed bigtime. A wet coop or run is an unhealthy coop or run. Wet poop stinks. Chickens poop a lot so if it builds up to any density whatever it will stink when it gets wet. Location, location, location.
The purpose of bedding is to act like a diaper, absorb moisture from poop so it doesn’t stink. It doesn’t matter if you use dirt, sand, wood shavings, wood chips, hay, straw, Spanish moss, dried leaves, or anything else. If it is in a pool of water it is not going to absorb any moisture. Your run needs to be able to drain.
A lot of us don’t have a lot of options when it comes to where we put a run for many different reasons. You have to play the hand you are dealt. When I built my coop I hauled in some dirt and raised the floor level a few inches so rainwater runoff does not go inside, then use wood shavings as bedding. It stays dry.
My run is on a high spot. It’s bare dirt. It still becomes a muddy mess when the weather sets in wet but it’s not that bad, I can easily live with it.
Another issue is poop load. The more chickens you put in a small area, the more the poop builds up. Some people, especially in suburban backyards where space is tight, are out scooping poop on a daily basis to keep it from building up. I use a different approach, in addition to my main run I have a big area enclosed in electric netting and covered with grass in the growing season. In my climate, they spend practically all day every day in that grassy area, spreading the poop around. A whole lot of people don’t have the room to do that.
Some people with small runs use some type of bedding and clean it out and replace it if it starts to smell.
As you look through the forum you’ll see that a lot of different people do different things. If the run stays reasonably dry a whole lot of things work. If it stays wet not many will work or you have to work harder managing it.
Some people use what they call the deep litter method in the coop or run. Basically that’s turning the run into a compost pile and let the chickens turn it for them. I don’t know if you have ever had a compost pile? If it is too dry the microbes and bugs that eat the stuff and turn it into compost can’t live. If a compost pile gets too wet it turns slimy and stinky. Your goal for moisture level is to have it a little damp. I’ve seen that ideal moisture level described as get a sponge wet then wring it dry. A compost pile can handle more moisture than that for a little while, but if it stays too wet too long it can become pretty bad. It needs to be able to drain. So does your run.
I don’t care what you use as bedding. I like it to be inexpensive and readily available, but if you want to use something exotic go for it. You only live once, at least in this incarnation if you happen to be Buddhist. Just try to keep it dry or where it will drain fairly well. You’ll be better off whatever you use.