Hi Kari- Joanne has pointed you in the right direction, and it is all about personal taste. I'm in no way a Copic expert, and I actually just started using the markers myself, but I'll offer you some combos that I keep turning to, time after time.
Browns- like Joanne- I too like the Brick Beige, Chamois and Dark Brown combo. I also find myself using Light Suntan, Reddish Brass and Copper combo too.
I would second the warm grays for mice images, but I would go a little darker for the cat images maybe cool grays for that. And start with a lower number like a 2 or 3 and then layer with a 5 or 7.
I also use the lowest numbers of cool gray for outlining/adding dimension to images.
I reference Marianne Walker's blog frequently for copic coloring tutorials and such. here is the link:
http://ilikemarkers.blogspot.com
best of luck to you!! its so much fun getting started with these markers. (Although I'm slightly addicted now) :-)