A6 is my normal commute – has been for 10+ years actually! It’s not the nicest road in the world but it’s generally OK and the volume of traffic means that you just kind of flow with it.
Watch out through Longsight – partly because it’s a total dump and partly because it seems to have the worst driving standards in Manchester and that’s a fairly low bar to begin with!
Stockport through to about Longsight you’ve got a continuous bus lane which helps a lot.
Just after Longsight, fork left down Plymouth Grove (A5184) then turn left through the university to come out on Oxford Road. That’s far and away the nicest route into town for cycling – protected cycle routes all the way and the road is only open to buses anyway.
You could just get the train, direct from Whaley Bridge, takes about 40 mins.
There are other cycling routes; the canal towpath runs from Whaley right into the centre of town but it’s slow, it’ll be 90+ minutes riding time on a CX bike.