I lived in South Wimbledon when I first moved to London. It's quiet, it's near Wimbledon proper and it's green spaces but it's no hub of excitement

That area down towards Morden/Mitcham would be fine. Personally I'd go for Tooting everytime. Got the Common and the Lido, but also all the pubs and excellent restaurants, good food shopping in the South Asian shops if (like me) that's your thing.
The Northern Line into town here is not 20 mins max! About 20 mins to Clapham Common, 30-40 mins into town. Depending whereabouts you are, rail may be a better option into town from Wimbledon/Tooting.
Had family who lived in Rose Hill growing up. Very white but changing as ethnic minorities move there for affordable houses with gardens, working class, mostly people who moved into new council stock from Wandsworth/Lambeth in the 50s and 60s. If you wouldn't mind living in very similar areas of Essex or Kent, and you don't mind quite a jaunt to get to anywhere "cultured" or any decent pubs or restaurants, it's okay. It is Chelsea supporter central, and there are lots of white vans, but at least with my family, that didn't equate to being rabidly right wing

I'd say if you haven't got kids and you occasionally will want to go out/get into Central London easily, Tooting or S.Wimbledon would be far better.