I prefer British English, but I definitely agree with Nef that you should choose which language to learn according to your future plans.
The British accent, by which I mean what you hear on the BBC, is infinitely easier to understand, so I'd advocate that for a new learner. It's easy too - just pronounce every syllable clearly, and you've got it.
American English would help those who are in the entertainment line, or want to "be cool".
My friends tell me I don't have an accent, which I take to mean that I have a neutral accent. Sometimes it veers towards the British, sometimes the American. But the greatest emphasis lies on speaking good, clear and grammatical English.
It helps to have a working knowledge of both British and American English, though. There are a few differences between the two that can be really startling when you first come up against them.