OP - you've got to bear in mind that 90% of people looking for a 4-5 bedroom house have exactly the same requirements as you, e.g. want good schools, a naice area and a reasonably commute to Manchester (or Stockport in the case of many of the areas you are looking at).
So anything that is cheaper than the average, which your budget is for that size of house in South Manchester, will most likely not be exactly what you are hoping for.
Postcodes are not the most useful guide for Stockport properties, as SK6 for example covers a fairly large area, and many different communities, all with their strengths and weaknesses. Marple is a nice place to live and bring up children, but a tedious commute with terrible traffic. Romiley is OK even up and coming, less posh than Marple but nearer the motorway. Woodley and Bredbury are even nearer the motorway but much less posh and not so much of a village centre.
Side note - As Stockport is city sized but actually still a town, then the surrounding areas tend to call themselves villages, despite being of a size that most people would consider towns. Some residents also like to consider themselves to live in Cheshire, despite Stockport having been part of Greater Manchester for many decades.
Offerton has very few shops or other services, I personally dislike the Bosden Farm estate heartily, lots of small roads circling in on each other but we all have different tastes. High Lane ditto. Disley likes to think of itself as a Cheshire village, it has a few shops and restaurants, but would be a nightmare commute by road. Most affordably houses are probably along the very busy A6. It can be a pain being right on the edge of the county, same for New Mills, Furness Vale and Whaley Bridge, which are a short distance further along the A6 but in Derbyshire.
As you have rated proximity to good shops highly, most of Stockport is likely to disappoint. Stockport town centre has sadly lost many of its large shops in the last decade or so, although it still has a useful selection, my daughter likes the big Primark for example. Manchester is a bit of a trek for many Stopfordians. The John Lewis at Cheadle Royal is useful, as is M&S at Handforth Dean, both on the A34.
Urmston is very handy for the Trafford Centre, shopping mecca for many.
Have you had a chance to come and look at any of the areas yet?