most protection (vs things short of a bear) hardware cloth on any opening larger than 1/2". If budget is an issue and you're mainly concerned about raccoons reaching in, then hardware cloth up the bottom few feet of the run only.
For the coop, any doors/hatches that open should have a 2 part latch, like a hasp with a carabiner, or a latch that locks shut (i.e. padlock).
Very good visual of an apron install here:
https://www.backyardchickens.com/threads/new-coop-project.1169916/page-2#post-18481208
You have a couple of options with the door. I use hardware cloth on the frame and the door so that when it closes, the layers of hardware cloth sandwich on top of each other:
View attachment 3239699
A similar effect would be the one described here:
https://www.backyardchickens.com/th...der-2020-version.1529488/page-7#post-25809665 Or you could fill the gaps with wood as previously mentioned.