Oh good grief, ignore the first two posters who clearly haven't a clue what they're talking about!
All the areas you mention are perfectly nice and perfectly safe. I live in one of them
. They don't have 'rough' areas at all - the only very vaguest exception might be 'south Croydon' depending on where you mean exactly as of course 'south' becomes 'central' at some point!
Sanderstead would be my pick if you have kids as JTro says. Nice villagey feel (duckpond, Waitrose, park, etc), handy shops and great primary schools, with Riddlesdown Collegiate/Warlingham School for secondary. Although it's probably the priciest of all the areas you mention.
Kenley and Purley have some beautiful houses and most areas are a wee bit cheaper than Sanderstead (although Purley can get very pricy too). Kenley doesn't really have a 'centre' and Purley's isn't quite so pretty, based as it is around a big roundabout!, but it's very useful for shops and buses.
Upper Warlingham is taking you a little bit further out - but again some lovely parts, very green, lots of big houses, two train lines nearby.
Riddlesdown is mainly residential with fewer amenities but it does have the benefit of tonnes of green space.
South Croydon is great for transport and restaurants etc but is more built-up and has a busier vibe. Still perfectly safe though, imo.
What's your budget?