"What should I be doing during the week?" "How often should I be working out?"
It would be okay, even advantageous, to start some mid-week cross training. On your rest days, you can cross train presuming the exercise uses different muscles than running or walking. Cycling, swimming and elliptical machines are all great exercises to do to help work lactic acid through sore muscles or keep different muscles active. Make sure you are doing some activities which work your core. Do the plank, crunches, ball work, what ever works the core.
Your core muscles help keep the body in alignment while you are out there on the road. A strong core helps keep you out there longer without injury. Make sure you are getting at least 3 days of running or walking in per week, in addition to our Saturdays.