New Malden is great, has everything you need, good location etc.
The flats you are considering are in an 'ok' area. I would avoid Kingston road further up near Kingsmeadow though (Cambridge estate).
The roads near Morrisons are fine.
The nicer parts are off the high street... The Groves (Acacia, Chestnut, Lime, Poplar etc). Dukes Avenue Malden Hill, Kings Ave, Alric Avenue (£££). Near Beverley park. Cambridge Road, Connaught & Cleveland. Other areas creep much higher up the budget (Coombe Hill etc).
There are larger blocks of flats off Acacia grove which have been there 50+ years (Linden court) , big floor plans, safe area. I'd prefer that over a new build on Kingston road.
Kingston road is very busy. It's near the hospital so is a route for ambulances & the fire engines. But if you're round the back it would be ok.
Secondary schools you'll be in catchment for Tolworth Girls, Coombe girls, Coombe Boys, & Southborogh boys, Tiffins if you want state grammar. Or Holy Cross & Richard challenor if you are catholic
I'd be looking at getting value for money. Maybe checking Berrylands, Surbiton, Hinchley wood etc.
What's your budget? That would help immensely!