From the city centre, I'd take the A34 as far as Parrs Wood, take Manchester Road B5095 to Cheadle, turn right on A560, over A34 to Gatley then Styal Road right up towards the airport. Or you could head further west, taking Palatine Road
Don't go further down the A34 than Parrs Wood - more like a motorway after that, hence the Manchester Road diversion.
Not sure what's best from Middleton to city centre though.