I'm in the desert and we LOVE sand on the floor. It's natural, it's free, it's dry, it's easy to clean, and the chickens seem to enjoy it. We get a bale of hay twice a year and rotate a flake every month or so in half of the run. I do the deep bedding method with the hay...chickens like to play in the hay. The sand is cleaned more often & much like a kitty litter box.
They'll go somewhere to get out of the rain usually in my experience. If they're not going to access the whole yard they should be fine.
I've never used the pellets, only pine shavings. Others have said the pellets work great though. Maybe try a search and see what people have said about them.
Does the area you're putting the run usually flood? If so I would put it elsewhere. Otherwise anything absorbent will work. Avoid straw, hay and anything else that will prevent the area drying out after the rain and you'll be fine.
If you're allergic to hay and pine,
and don't want to clean poops daily, that really limits you.
I was about to suggest sand, which I rarley do,
but in a desert clime it works.
You could do a deep litter without pine or hay.
There are many other plant materials that would work,
just make sure you have a good mix of sizes and shapes,
too much of anyone material can cause problems.