Walls and Ceilings - Mold on my drywall and studs

I'm remodeling a bathroom and I found after I took out the drywall I have a mold/mildew problem on the studs and drywall. It isn't terrible and the drywall has not rotted out, but I'd like to arrest it before putting new walls up. My idea was to sand the places where there is mold on the studs and then seal it with a urethane coating. I'm not quite sure what to do with the mold spots on the drywall paper. What do you think of my stud plan and any suggestions for the drywall paper (both killing it and sealing it against future growth)? I live in Austin so it is humid enough for it continue if don't get control of it now.

I've seen a lot of mold in North East Pennsylvania mostly from leaky pipes, but your situation is about the same... And my answer which I always tend to play it safer then sorry is to gut. I've been told that once mold hids wood, you can't get rid of it due to wood being porous. You could just get away with just cutting off the bottom few feet of board and sistering one in next to it... If the plate is moldy then it should go too.

If it's begun to attack the drywall do you'll want to atleast get rid of the moldy sections.