To clean the coop:
Sweep it out, then go over it with a wire bar-b-que brush (I am assuming the coop is raw untainted wood).
Next, you can decide how hard core you want to be, you can spray it all down with some product you find in the feed store designed for the sort of thing, or wash it all down with a bleach solution (so much bleach mixed with so much water). The more bleach to water the stronger the solution.
The nice thing about bleach is that it is pretty cheap, and it breaks down quickly, so there is no toxic residue.
After all of that cleaning, and after it is all dry, I would paint the inside, unless you first want to insulate the coop and put in poop boards, exterior nest boxes, and such very nice stuff and then paint.
As to the run, chicken wire and wood boards aren't too expensive. I would put up a frame over the run and some chicken wire over the entire thing, but then I have lots of raptors.
Also, being the house while the chicken roam is not adequate protection. Chickens are super tasty as well as very easy to kill. All my kids and husband were outside working when a dog broke into the coop and killed my flock. They didn't notice. I have been outside watching the chickens and watched as an eagle attacked. Even though I ran up screaming, he had pined her down before I got up close and scared him off.
Good luck, and totally awesome that you have such a great coop and run to work with.
Look through the coop pictures on this site, it will give you lots of ideas as to what you might want to change before you get a flock.
