Are you coming up from Milwaukee direction or more southbound from Illinois (I assume more southbound)?

Getting around Madison, if you choose, can be done via the Capital City Trail. If you are not averse to crushed limestone, you can get from the Illinois border to that trail (which is paved) via the Badger Trail in Wi and Jane Addams trail in IL.

With regards to the county maps, nearly any county road will be a good choice, particularly west of Madison (they could be pretty busy before that, and east). The County Roads use letters.