What is the proper personal protective equipment and procedures for removing mouse nesting that may contain Hantavirus?
Generally, house mice don't carry hantavirus.  However, it sounds like your property may be semi-rural, so there might be deer mice, which may carry it.

I found this Center for Disease Control PDF.  Interestingly enough, it doesn't talk about respiratory protection at all.  It seems that all you need to do is spray down the old nests/etc. with disinfectant or a bleach/water solution and bag it.

While I don't claim to be more knowledgeable on the subject than the CDC, I would certainly wear a mask.

Summary from PDF for posterity:

How to clean out cabins, sheds,
barns, or other outbuildings:


Open all doors and windows. Leave them
open for 30 minutes before cleaning.
Wear rubber or plastic gloves.
Clean up all rodent urine, droppings,
nests, or dead mice or
rats by using a
disinfectant or a
mixture of bleach and
water.
Air out cabins
Mop floors or spray dirt floors with a
disinfectant or mixture of bleach and
water.

Clean countertops, cabinets, and
drawers with a disinfectant or a
mixture of bleach and water.

Steam clean, shampoo, or spray
upholstered furniture with a detergent,
disinfectant, or a mixture of bleach and
water.