Where are you going to be working in Manchester? Use that to guide where you choose to live. The trams (Metro) have changed how easy it is to get around the city from the dark days of having to rely on buses and trains alone.
Like folks say, north manchester & further are great for lancashire, the pennines, the western dales, and the lakes. Pick your area carefully.
South Manchester (Didsbury, Withington on the other hand & over the border in Cheadle, Cheadle Hulme, Bramhall is great for the cheshire plains (!) and getting into the Peak District. There’s riding out the door from these places towards Poynton, Lyme Park & onwards.
In north Manchester if you’re off the tram route getting into Manchester can be a pain. In south Manchester once you stray south of the Mersey or east of the A34 your public transport options shrink too unless you’re close to one of the railway stations to Piccadilly.