Great question, read this. The best time to fix a muddy run is before you build it.
Pat’s Big Ol' Mud Page (fixing muddy runs):
https://www.backyardchickens.com/articles/how-to-fix-a-muddy-run-chicken-coop.47807/
There are two potential issues with the run being wet. To me the less threatening is that if it is on clay a wet run turns to a muddy mess and you said you have clay. If the chickens can't get out of the wet at least part of the time they can develop foot problems. A wet run can potentially become unhealthy as certain critters like the bugs that cause coccidiosis thrive in wet conditions if poop is present. And those runs are a mess to walk in. They are just not nice to be around or to deal with and can pose a hazzard.
The other issue is that chickens poop. When chicken poop gets wet and stays wet the microbes that eat it become anaerobic (no oxygen). The water keeps the oxygen away when it is really wet. Anaerobic microbes digestive byproducts stink. It's like a compost pile. If the compost stays slightly damp the aerobic microbes do the job of breaking the compost down and it has a nice earthy smell. But if the compost pile gets wet and stays wet in a few days the anaerobic microbes take over and it smells horrible. So keeping the coop and run fairly dry or at least getting it to dry out fairly soon after it gets wet is pretty important in my book.
If you dig a hole in clay and fill it with sand, water will not go anywhere. It has no place to drain to. If you build the sand up high enough it may not get muddy, at least for a while until the sand disappears into the mud, but it still has the potential for stink.
I personally use aprons for dig protection instead of a layer of wire underneath but do it as you wish. If I were in your position I'd consider hauling in some more dirt to raise that run area above the surrounding land if you need to so the water has a place to drain to. I have no idea how much if any you need for that. Then I'd put sand on top. Sand drains really well as long as the water has a place to go.
Chickens scratch a lot. Rainwater can wash sand and clay, especially loose clay. You probably want to put some type of barrier around the inside bottom of your run to hold the sand and clay in. Use whatever you want for the barrier. It would be nice if it allows for drainage yet hold in the clay/sand. Different kinds of wood, maybe wire mesh, plastic edging, even a row of cinder blocks.
Sand does tend to disappear into clay over time. Rock will also but more slowly. It would probably be a good idea to put a layer of gravel on top of the clay and under the sand to slow that process. The chickens will probably scratch down to the gravel so I'd suggest some round rock like pea gravel or river stone that has been smoothed over time. Crushed gravel could have sharp edges that might cut their feet. Not that it happens each and every time but I consider it good practice to try to avoid things that can cut their feet when they scratch.
Instead of sand you can use some type of bedding directly on top of the clay or even on the gravel. We all have our favorites, not surprising as we all have different conditions. Some things might work better for some than others. Having a ready inexpensive supply might be important. The way we manage it can be a factor. People use wood chips, wood shavings, straw, hay, grass clippings, dried leaves or other things like peat or Spanish moss. Your main restriction is your imagination and what is available. I don't think Spanish moss will be that available in Pennsyltucky.
Chickens poop. The more chickens you have pooping in a small area the faster it builds up. If it builds up faster than it decomposes it can get too thick and stink when wet. Some people with sand manage this by using a scoop and regularly removing clumps of chicken poop. You may need to occasionally remove whatever bedding you use, sand or any of the others. We are all unique, we need to stay flexible.
I agree, get construction moving as fast as you reasonably can. Life has a way of messing up construction schedules. I'm not sure what your weather will be like when those chicks are five weeks old but they should be able to go out without any supplemental heat by five weeks. If your coop were ready and you could get electricity out there you could even brood them out there straight from the post office or much sooner than five weeks. That's worth a separate thread if you want to discuss it in detail. Many of us do that even when it is below freezing outside. Your coop will probably be bigger than your brooder, you are correct that they will enjoy that even without access to the run.
Good luck!
Glad it was a misstype, but I'd rather point it out than to find out later that some coon reached in and snatched a favorite bird.
