Wet is your enemy, coop or run, no matter what bedding you use. Wet poop stinks after a couple of days. Whether you use dirt, sand, straw, hay, wood shavings, wood chips, Spanish moss, dried leaves, or something else the chickens are going to poop on it. It will build up to the point that if it is wet it will stink. To me the best bedding is what you have on hand and isn’t too expensive. In the right conditions they will all work. In the wrong conditions you can have problems with any of them.
The purpose of whatever bedding you use is to act like a diaper, absorb the moisture from the poop so it dries out. If it is wet it cannot dry out the poop. If your run is in a low spot that collects and holds water, you are going to have problems. If it stays dry or dries out pretty well you have a lot fewer problems.
I never have to clean out my coop bedding. I do once every three or four years, not because I have to but because I want that stuff on my garden. I use droppings boards to collect the majority of the poop from under the roosts and use that in my compost. I keep my coop really dry. My climate is such that my chickens spend most of every day outside instead of in the coop so they are not dropping a lot of poop in there. My chicken density is fairly low, I don’t over-crowd my coop. I use wood shavings because that is the least expensive thing I’ve found. There weren’t any trees here when I first moved here but I’ve planted several. Hopefully in another year or two I’ll have enough dead leaves to use some of them at least part of the time.
Some people clean the bedding out of their coop weekly, some less often. Very few go as long as I do. Frequency depends on a lot of variables, a lot on how dry you keep it.
If your run is high compared to the surrounding area so water drains from it, you may be in great shape, but it is really hard to keep a run of any size really dry when the weather sets in wet. My 12’ x 32’ main run is on a slight rise and I put a swale on the upslope side to divert rainwater run-off. It’s dirt and it drains pretty well, but when the weather sets in wet it becomes a muddy mess. It doesn’t stink though, I have a large grassy area inside electric netting where they spend most of most days and spread the poop out. It’s not concentrated. The chickens do not spend any appreciable time in that muddy run so I can live with it. I never clean my run.
If your run is a low spot where it acts like a swimming pool and holds water, you can put all the sand you want and the water will stay there. You can put all the organic bedding material you want and the water will stay there. The poop will build up and it will stink. You don’t want your chickens spending their life in wet, it can damage their feet, so having something up high enough to keep them out of wet is a real good thing, but you may be cleaning any bedding you put in your run out on a regular basis.
When I built my coop, which is on the ground, I hauled in some clay dirt and raised the floor level a few inches to help keep water out. If your run is in low spot you might want to consider doing something like that. Build it up so the water can drain out before you start adding bedding.
Some people use their coop or run to make compost, that’s sometimes called the deep litter method. I can’t do that in my coop because I keep it too dry. To make compost the litter needs to be slightly damp. If it’s too dry the bugs that eat it and turn it into compost can’t live. If it gets too wet it will stink, but so will a regular compost heap, whether there is chicken poop in it or not. Any organic matter will stink after a while if it gets too wet, chicken poop is so high in nitrogen content it doesn’t take long for it to get to that point.
Your issue is going to be water much more than what bedding you use. You may have to change it out regularly, you may not. Your nose will tell you that. My suggestion is first to look at any drainage issues and address that. Then try to find something available and relatively inexpensive in case you do have to change it out regularly. And look at how much hard physical work it would take to change it out.