First, take a deep breath
Mice are not going to hurt chickens; rats can (I'm pretty sure I had a chicken who was in a dog crate 'jail' for a few days get her feet nibbled by a couple rats that I know for a fact were in the bldg at the time) but honestly both of them are more of an issue for PEOPLE than for the chickens. You don't need a larger mouse population around than can be avoided, and you
really don't want to be ranchin' up rats (which can become a very serious problem if they start getting into peoples' houses).
As far as mice go, some will probably get into your coop at some point, oh well -- the main thing is just to avoid creating somewhere they can set up a little hotel and have thousands of offspring, and to keep them out of the chicken food as best possible. So, if you insulate the walls, make it with TIGHT carpentry, and avoid having any other little enclosed spaces where mice might like to live (see below).
Now as for rats: are you in an area with a known rat problem? Or is there no particular evidence of rats at work there now (although that doesn't mean some may not become more interested once you have chickens?
If you KNOW you have a significant rat issue already, then you will for sure want to take extra steps to ratproof the coop. This is the one case where I would advocate burying a 1/2" or 1/4" hardwarecloth "floor" in your run (under at least 6-8" of dirt or sand, so the chickens can still enjoy themselves), and using hardwarecloth for the entire run (nothing larger mesh). Having your coop, and maybe even the run also (again, topped with sand), on a concrete slab would be even better if you can afford it. Then build everything with VERY VERY PRECISE TIGHT carpentry so there are no gaps; either put the coop directly on the ground or raise it 18" or more, so that rats are disinclined to hunker down underneath and chew their way in; and consider running metal flashing over all exposed edges and corners, at least up to 2' or so above the ground. Make sure popdoors are constructed so rats can't chew their way in, too. It can be done, but it IS a bit more work.
However, if you do NOT have any particular reason to believe there is a large active rat population around, just do what everyone else does. Use some common sense
, build the coop either directly on the ground or raised at least 18" for the reason described above, make your carpentry tight and don't create little secure spaces, try not to leave feed outdoors at night, and then just see what happens. If you start seeing evidence of rats, you can retrofit things by lining the floor of the run with pavers or hardwarecloth, putting flashing on gnawable parts of wood, etc.
Oh, and the biggest thing of all in avoiding rats (and excessive mice) is: don't let them start considering your yard a buffet. Always, always, keep all feedstuffs in SECURE containers e.g. galvanized trashcans with a bungee or chain on the lid. Preferably indoors. If you're worried about rodents, put your feeder IN the coop not outdoors, and be wary of putting any bedding that has large feed spills in it on the compost or garden as that is how I acquired MY first (and only, and AFAIK now totally *former*) rat problem
Honestly though, for most people, rats are a non-issue and mice are at worst a minor nuisance.
Good luck, have fun,
Pat