It depends entirely on your budget. Obviously, as a young professional, you'll want to be close to the centre of town, for all the bars, clubs and parties, but not close enough that your rent is astronomical. The good thing about London is that if you have your heart set on living in a particular area, with the fluctuating price ranges from one neighbourhood to another, you may not be able to live right in the area of your choice, but you can probably live a short walk, or a tube stop or two away.
So, with regards to areas, here's some brief descriptions which might help you pick:
Camden: used to be a great centre for alternative (rock, metal, goth, punk, etc.) scenes, and, of course, the home of Amy Winehouse and other creative people, but that has now dwindled somewhat into a more tourist area. Still some good places to live, with a number of pubs, bars, restaurants and clubs.
Shoreditch: very arty and trendy (yes, with plenty of hipsters!), lots of cafes and bars, large amount of creative and media companies.
(by the way, bad on what I read about Prenzlauer Berg, the above two might suit you best)
Kings Cross: a transport hub, currently undergoing a lot of development, but with companies such as Google moving in, a lot of investment is going into the area to the north of the station. Useful if you want to get anywhere.
Clapham: Quite a trendy area, with lots of families, green parks and so on, not sure about the entertainments, as I don't go there very much, but there are a number there, if not a little busy at weekends.
Hope that helps!