Which variant of English should I use when my target audience is the world?

If your target audience is the world, then you target not only people with a knowledge of American English, British English, and so on, but also people like myself, to whom English is not a mother tongue but a foreign language. If reaching these people is important to you, then you might want to write in a relatively simple English, avoiding not only regionalisms, but also:

• Idioms that are hard to understand; e.g., some sayings are not trivial or use unusual vocabulary. As an example, I'd say that “a bitter pill to swallow” is rather straightforward to decipher, even if you have never encountered it before. “An axe to grind”, on the other hand, is harder, probably because it refers to a situation that you is not part of daily life (for most of us) anymore!
• Vocabulary that is out of the ordinary; for example, even though the many words describing different ways to hit or strike (something or someone) express different nuances, “hit” or “strike” is easier to read than “batter” or “thwack” or “clobber”.

Overall, providing a lot of context, and writing simple, concise sentences will help make your point clearer (and not only to “foreigners”).

I would suggest writing in the version of English you are most comfortable with. That's what you'll communicate in most clearly, and everyone else will understand it from that domain.

English is broad church (British English bias intended :).

My preference in many circumstances would be to not unnecessarily burden yourself with removing any regional colour from your English writing. Seeking to do so will eventually only make English into a more generic and less expressive language. If the writing is online you can always make a helpful hyperlink or two.

It's important to be easily understood, but that's not the only important thing.

The answer to this is included in Postel's Law: “be conservative in what you do, be liberal in what you accept from others”.