The tarps I use are the brown and silver ones from Lowes. I think they are 15 to 20 mil so not the cheapest. My coops here are basically runs that are 2/3rds covered by tarp.
Mud in the pen is minimal after useing the big chunk mulch. The pen the tarp came off of has pea gravel as its base. I still need to mulch that pen.
I usually use a tarp that covers top, back and one side. The replacement only covers the top I think its a 12 x 16, the one that was on the pen was a 16 x 20. It covered the top 2/3erds, down the back side to the bottom and down the left side(north side) to the bottom. I did use another tarp on the north side to block some of the wind.
My pens are 9ft wide by 18ft long and 6ft high. A metal frame that has a curved top and covered by hardware cloth. With being on the Texas coast these are just easier to deal with. Heat and humidity are my biggest battles down here vs. winter weather that we have little of.
The tarps last about 3 to 4 years. They would last longer if I bought the good heavy canvas ones but they are super expensive. Like $200 for a 12x16.
I think I covered all the questions.
Oh hardest part on this replacement was moving the second pen I have attached to the main one as they are the same size.