The deep litter method is intended for a dirt floor coop, in case you did not know.
I have two dirt floor coops. One was not built to be a coop, is too low, and stinks when it gets wet. We had over 14 inches of rain in the past week, unusual here. I added lots of litter to get the smell under control and give the hens something dry to walk on. The other (new one) was planned as a coop, and several inches of dirt was added. The dirt got damp during this rain, evidently just because all the dirt around it was wet, but will dry out in a day or two. I think it's going to work OK.
If you go with dirt, I'd recommend you add plenty of dirt to raise it above the surrounding ground, as you will find yourself removing some when you clean. I figure I'll have to add dirt once or twice a year to the new one. Plan to phase the old one out.
On the run (fenced field for me.) I read here that about 87 sq ft per bird is what is needed to maintain grass or other vegetation in a run. Since 10 sq ft per bird is considered sufficient on BYC, I see why most people's runs turn to mud. My field will provide this kind of square footage; maybe yours will, too. Curious to see this summer whether vegetation can still grow!
Good luck, whatever you decide.