You're looking at some attractive areas and (given you're not rush hour commuters) not far from Manchester at all by car or rail. Most people I know in the areas I list below (at least those in Cheshire) work in Manchester or the outskirts.
For those who want fresh air and green space it's worth remembering that trains from places like Prestbury, Alderley, Poynton etc take the same length of time into Manchester as the tram from more built up areas such as Altrincham/Timperley. Less frequent of course and more expensive for that late taxi back.
If you draw a line from Marple/Marple Bridge down through Poynton as far as Henbury (west of Macc) then East of that line is basically where you start to feel there are hills! I am a hills person living to the West of that line and often wish I could bring the hills a little closer!
In your shoes I'd be looking at places from which I could get a train into Manchester (they all go into Piccadilly from this side so that works for your daughter) and accessible for Stockport or Macc (your obvious options for fast trains to London)
Bollington is hilly and is a good size in that it has most things but isn't large enough to feel built up. You're a short drive to Macc for the train (into Manc or to London) but Bollington itself does not have a train station which may be quite a negative compared with other options.
Adlington/Pott Shrigley border is lovely, green and hilly. Adlington has a station (2 stops to Macc for London trains; direct to Manc Pic in ~30 mins) but only has a pub, no shop or other facilities. Your closest shops are Poynton which is OK but doesn't inspire me (see below!)
Poynton has most facilities, a good train to Manchester and an easy change at Stockport for London trains. You need to be East (or Higher) Poynton to see much in the way of hills which puts you a fair hike from the station. Poynton itself I find fairly bland to be honest - both the centre and the broader housing stock. Higher Poynton/Middlewood Way are very pleasant though.
I'm a big fan of Marple Bridge and Mellor. Beautiful surrounds, good Parks (there and by Compstall), selection of cafes/eateries (MB) and some great pubs (Mellor) as well as the train in. Marple isn't as attractive but gives you more facilities (library etc). From all you've said I would definitely look at Marple Bridge. Drive into Manchester as previously mentioned isn't great.
Disley is attractive and has a station (& Lyme Park of course). It's slightly further out so the train takes a little longer. The drive into Manchester from Disley can be agony. The main road through Disley also carries many lorries so the noise detracts slightly.
I don't know the likes of High Peak, Buxton or Whaley Bridge well (passing visits) but would say you are getting further away from Manchester. If you're going there every now and then it isn't a problem, if planning to go in frequently then it's probably a consideration.
Macc itself is perfect in many ways. you get a ~24 minute service into Manchester 1hr 40/50 to London, all the facilities you need (given Manchester is no time away when you want more) and ready access to the hills. It can surprise you as it's fairly quirky in places (art festivals etc). Despite all that (& having lived outside Macc for a number of years) I can't recommend it as it does have that slightly tired, slightly short of cash market town feel. Also isn't green/trees/hills without living in a surrounding village
Probably worth visiting Prestbury although it's not an obvious choice for you. You are unlikely to get rolling hills from your window but it does have a lot in the village for its size, a decent train to Manchester, taxi from Macc for the London trains, and no more than a 10 minute drive to the other side of say Bollington. It's "Cheshire" money of course. You can afford it but may not want to. Very pretty village though and pretty good Indian (my priorities laid bare!)