Hi there. I stumbled across your post when I as looking for recommendations for a tiler local to me. I don't know if you've already decided or moved, but in case not....
I live in Ewell, just outside Epsom and until recently I worked in Kensington (retired now - yay!). I'd recommend it. Ewell West station is in Zone 6 (Epsom station is outside the TFL area). The trains to / from Waterloo run around every 15-20 minutes. My commute to High Street Kensington used to be about an hour door to door: 10 minutes walk to the station; Southwestern train to Wimbedon Main Line / Underground Station; change to District Line and straight up to High Street Ken.
I don't have children but my neighbours do and the choice of schools and child-related facilities around here appears pretty good. There's an old-fashioned tea room/ sweet shop in the village high street, as well as a Costa Coffee Shop which seem to be hubs for mums. I know it's a way off, but it's in the catchment area for a very good boy's secondary school (Glyn).
Housing in Ewell village itself is pretty pricey, but I moved from London 15 years ago and chose a street just outside the village and I love it. I'm lucky enough to back onto the Hogsmill Open Space - it's a nature conservation area, and it's just like being in the country. There's a river (the Hogsmill) and wonderful walks and cycle tracks. Part of it is currently being developed into a wetlands area which will be fabulous. There loads of wildlife around, plus you've got Epsom Common, Horton Country Park, and Epsom Downs for walking etc. Chessington World of Adventures is nearby, and Hobbledown (animal-based) is even closer. Farther afield are the Surrey Hills.
I'd suggest you look at West Ewell, but be picky about what streets. West Ewell covers a massive area and I'd suggest you look from Station Avenue to no further than Chesterfield Road. After that, you're getting pretty far from the station. The High Street in Ewell village is pretty, but for M&S, Boots, Wilko etc you'd need to go into Epsom itself where there's a decent selection of shops. For groceries there's a massive Sainsbury's midway between Ewell and Epsom.
Stoneleigh is also popular but a bit dearer. To me it's just rows and rows and rows of (nice) houses and there aren't as many open spaces and none as natural as the ones mentioned above. No idea about schools etc. There's decent local shopping - Co-op etc - on the Broadway next to the station (one stop up from Ewell West in the London direction). Some of Stoneleigh is in the borough of Epsom and Ewell / Surrey County Council, and some is the London Borough of Sutton so you'd need to be aware of that.
Although Ewell West to London Waterloo is about 30 minutes, for London style shopping, Kingston's not far and parking there is a cinch. The John Lewis in Kingston isn't as big as Oxford Street but all the other shops, e.g. M&S can beat anything in London. The Bentalls Centre is excellent and contains the Bentalls department store (part of the Fenwick chain so the fashion is great). There's also an outdoors market and plenty of one-off type shops. Personally, I think Kingston is better than central London. The range is as good, it's all in a small area, it's largely pedestrianised and although It's busy, it's not like central London where gaggles of tourists wander about aimlessly. Ikea at Croydon is about 30 minutes drive away.
(Phew! I didn't mean to go on for as long.)