In terms of working central Manchester, needing to get to London I would say it doesn't make a lot of difference moving in closer to Manchester, if you intend to travel by train rather than car. Everywhere mentioned is within 30mins train journey of the city centre and the centre has a free bus service. The only exceptions are villages of Appleton etc mentioned below which are in the region of a 50 min drive in rush hour.
If you choose Knutsford be aware the reason its slightly cheaper than some other places is because its directly under the flight path for Manchester Airport. It CAN be noisy depending on where you are. The surrounding small villages are nice but the price shoots up. The town centre is lovely - very old and quaint. It avoids the generic high street shops. It also has Booths Supermarket which is a local supermarket which has an extraordinary reputation (though can be expensive). The school from what I know is decent, but there are better ones in surrounding areas.
Didsbury is not so much a family area in my opinion. Its more studenty / singles and couples in their late 20 / early 30s. Heaton Moor tends to be slightly better option for young families.
Villages of Appleton, Stretton, Stockton Heath, Grappenhall, Thelwall and Lymm all have their own characteristics and are v nice (but can be pricer than other places mentioned here). Good schools. They are also very good for motorway links but have virtually no public transport links.
Wilmslow is very nice. Its definitely attracts slightly older families and not couples. It can be pricey, but you can get properties cheaper than in the villages of Stockton Heath and Lymm. Train station is well connected - better than Knutsford in that respect. And it doesn't tend to suffer the over head traffic problem from Manchester Airport. Its not as quaint as Knutsford though.
Alderly Edge. Very nice, but I think you'll find your money will go further elsewhere.
Bowdon / Hale / Hale Barns are lovely, again pricey and very much in demand. Good schools.
Bramhall and Cheadle aren't bad choices. They are more suburban than a few of the other places, but schools and trains are good and you could do a lot worse. I guess they lack a little of the character of some of the other suggestions but then you pay for that and theres nothing wrong with them by any means. Again, trains are good. Really depends on your budget and whether you want to pay for the charm of other options.
Macclesfield and Bollington. Honestly? Bollington is lovely, but on the edge of the arse end of no where. I think they are just that little bit too far out for what you are looking for. Weather in the winter in Macc can be 'interesting' due to the far its just on the edge of the peak district.
All in all, its a really good area to live and has as much to offer, if not more than many places near London. To be honest, you can't go far wrong with most places mentioned on a budget of £350k. Wish I had that much!