This will be an essay lol
Tbh, I wouldn’t move to Wallington for schools unless you’re churchgoers (very mixed primaries and a secondary blackhole if your children don’t get into grammars).
Around Carshalton Beeches, if you’re near/North of the station, you’ll be in a perfect spot for walking to the countryside but also close enough to Carshalton Village for another station(Thameslink + quick Victoria trains), a great leisure centre and the shops on Banstead Rd or the Village high street + a bunch of tennis clubs and other things (Scouts, ballet etc). The big houses further south of CB station (Beeches Walk and beyond) have fewer amenities close by so depends on what you’d need regularly.
The primaries that side of SM5 will be fab, back up secondaries ok rather than wow unless you’re close enough to Harris Sutton (new no GCSEs yet but already v oversubscribed with a Science specialism). Overton Grange is alright too but for whatever reason tends to be undersubscribed.
In SM2, you could try the CB side, eg the gorgeous Edwardian ‘Windebanks’ on the Ridgway. That’s near the shops on Banstead Rd for a ‘villagey’ vibe but also easy for all the amenities in Sutton (cinema, gyms, yoga studios, shops and restaurants and the really good station with direct links to Victoria, London Bridge and St Pancras).
The roads around the Downsway are ‘prime Sutton’ and will be mostly over budget but some houses sub 1.1M do come up. Again easy for the town centre + the Banstead Commons for country walks (footpaths to the lavender fields and the farmland south of Carshalton too).
Then there’s the Belmont Village area, edge of countryside, mini high street but the train station is pants so you’d want to be within walking distance of Sutton or Cheam.
For a stunning period property in a beautiful area, there’s the Landseer Conservation Area (Landseer Rd and parallel roads between Sutton and Cheam Stations). That’s SM1 but the best for amenities if you want everything a short walk away. It’s the only bit of the bunch that makes the v desirable Cheam High catchment in case grammars don’t work out.
Finally, South Cheam is SM2 as well. The trains go into Victoria and London Bridge. It backs onto the Banstead Commons. Cheam Village feels the smartest of the bunch with a Waitrose and independent shops + Nonsuch Park is an old Henry VIII’s one with a similar vibe to Richmond Park. You’d get rugby, cricket and plenty of tennis clubs, a David Lloyd, Nuffield Health etc. South Cheam is too far from Cheam High but plenty of it will be close enough for Harris Sutton.
The primaries are v good across the postcode.
Finally, with regards to pricing, the areas are pretty cheap for the size of house you get for your budget. I would say most houses will need work. If you’re not sure about spending the full 1.1M, you could still get a 4-5 bed semi in one of those areas for 800-900k (incl all work) and invest the rest elsewhere.