Check and seal all possible entry points. Mice can get into spaces as small as a dime, but use some foam insulation spray to seal any small entry spots.
In regard to the mice, use your basic mouse trap with a small rolled-up piece of bread with peanut butter on it. On a recent camping trip I noticed mouse feces near the stove. I put two traps out and got one that night and two more over the next day. No more after that. Also, I just read an article about mice and an "expert" said the basic mouse trap made of a piece of wood and wire spring is the best for killing mice. I agree.
A while back I had red squirrels in the ceiling runs of my 5th wheel AC. They did some electrical damage that cost $1,100 to repair. (Most of the cost was labor for removing the ceiling to check and repair the wires.) To seal the entry points someone on this site recommended foam insulation with small chuncks of steel wool poked into the foam before it hardened. Later I found evidence that a squirrel tried to reenter at the point I blocked w/foam, but ran into the steel wool and gave up.