Amersham-born person here, moved back to bring up children. Beacon is lovely - my two older boys went there. Back in the day, girls at Heatherton had tea with the Queen mother at Clarence House once a year, in the summertime. It’s more academic these days but still looks like a well-kept school for well-kept girls :)
New Road has bargains because it is close to the council houses. Lots of bombed-out London families were moved there after the war and in the 1970s, there was still a painful social separation between the better-off Chesham Bois families and the council house people. Less so now: lots of Polish & Chinese families in the ex council houses, ambitious for their children, well-integrated. I know a very high-flying City mother who lives on New Road - it’s on the up.
Houses in the Mortens Wood/Sheepfold Lane area seem to suffer a lot from damp. Could be that there is a watershed in the ground there, hilltops in the Chiltern have them from time to time.
Old Amersham has some beautiful period houses, but bear in mind that houses on the Misbourne side of the high street can be hard to insure (flood risk), and some sinkholes have opened up along the course of HS2, which runs beneath the old town. Perhaps because there are expensive houses up on the hill as well (and a large council estate in the old town) there is not much of an old town: new town divide to speak of.
School wise, then: you go for private the one thing you will have to deal with are crazily wealthy people in £2m houses on roads like Bois Avenue & the like. This emphatically should not put you off choosing the best school for your child, but it’s as well to be prepared for the culture. If you can find families with similar priorities to your own (good schools first, affordable housing second) then the solidarity will help to carry you through the school gates scene.
Stoke Mandeville is not the best place to have a baby. I’m actually a qualified doctor (SAHM currently) and the sheer scale of clinical negligence there when I had my youngest was astounding, even by NHS standards. Cut into an artery on c-section, missed the resulting internal bleed, misdiagnosed the resulting faint and exposed me to needless radiation by doing an (unnecessary) lung scan. Then left me on an open ward while I was too radioactive to be near my own child. They were very skilled at covering up their errors however. If I had my time again & was planning as carefully as you guys are, I would take out an insurance package & go to one of the private London hospitals!
On a more cheerful note: I have loved bringing my children up here. With teenagers the place really performs well too: safe streets for going out to see friends, lots of sports going on at the new leisure centre on Chiltern Avenue (the swimming club here has always been a big feature), a good peer group.
Sorry for the scary hospital story, but I do hope all of the above helps.