As a rule, I implement all BSI (body substance isolation) precautions when handling any dead animal, just as I always did when dealing with human patients. Always better safe then sorry.
Latex gloves, sometimes two pairs. It's easy to carry a pair in a baggy in your pocket.
When skinning, I use the gloves, plus a rubberized apron.
In taxidermy, I use a clear face shielf to prevent splash exposures because I'm usually right there over the gore at that point.
Always wash your hands with a good disinfectant when done handling anything, and I always keep a pair of rubber boots for the skinning shed that are taken off before entering the house.
Do not take intact critters into your home. Those fleas will be looking for a new host and it may turn out to be your kids, your wife or you.
Make sure your dogs are up to date on all their vaccinations and wormings.
It's really very simple once it becomes second nature.