Have you just got your F1 post?
There are plenty of fine places in south london to live, indeed i live here now and still love it after 7 years. If you are working at King's / Thommies or Guys then i would say being close by is fantastic. Elephant and castle has the best links - on every bus route, 2 tube lines and an overground and is fine. It has a bad rep but i've lived here 7 yrs problem free. It's about 5-10 minutes from any of the above hospitals on bike and is dead cheap for Zone 1. It's also a 20 min walk to all of the southbank (waterloo / westminster / tower bridge etc)
Failing that Brixton, has ok links (1 tube line and an overground)and has a fairly decent vibe - nice restaurants in the old indoor market.
Vauxhall and Kennington are a bit dearer and slightly further away than E&C. Camberwell green / peckham rd is getting trendy but has crappy access (only buses). Streatham is a bit of a hole and i wouldn't bother (although some bits edging onto the common are nice). Herne hill / Tulse hill have overland trains and buses which are ok in the wk but infrequent at times at the wk end, have some friends live out there and they like it. If you want to go further out east Brockley and Greenwich are quite nice, New cross has a slightly bohemian trendy vibe and quite nice ladies (Goldsmiths art college is there). If you are inclined to go west it's more expensive than east..If i were you i'd avoid clapham like the plague, it's way overpriced and quite a good place for muggings as all new londoners move there. Your best bet is go visit lots of areas, get a feel for it and decide what you want (location vs amenities vs cost vs overall vibe) and make a decision from that. All areas have good and bad bits so go with an open mind... But most of all good luck!