American English or British English? Or perhaps Oxford spelling? Does it matter which language you choose? Do your readers care?
Obviously, if you write for an American audience, you should write American English. And if you want to send a paper to a British journal, you should use UK English, which is another name for British English. Always check with the publisher or read the style guide of the journal. However, it is crucial that you are consistent and write your whole text in one and the same language.
When you write a doctoral thesis or a novel, the choice of language is yours. Only, as I said above, be consistent.
If you go for American English, use American spelling and write labor instead of labour, center instead of centre, catalog instead of catalogue, fulfill instead of fulfil, traveling instead of travelling, and so on. Use a z instead of an s in words like recognize and organization. (There are, however, some words that are always written with -ise or -yse – read more about them here.)
American English uses the serial comma, which is the comma that is placed before and or or in a series of words. An example: Horses, cows, and sheep are farm animals. British English does not use this comma.
There are also differences in vocabulary. The American apartment is a flat in Britain, Brits walk on the pavement, while Americans use the sidewalk. And when you are angry in Britain, you are mad in America – to a Brit mad means crazy. When something is quite good it is very good in America but only fairly good in Britain.
There are, of course, also differences in grammar. When a British speaker uses the perfect tense, I have already called him, an American would use the past tense, I already called him. The American a real good movie is in British a really good film.
Oxford spelling is a variant of British English. It prefers -ize in words like organize and recognize instead of the spelling -ise in British English. The spelling with -ize is actually the oldest; organize, for example, appeared in a text in England as early as around 1425. The Oxford spelling is used by publishers like Collins, Longman and Oxford University Press (but not Oxford University!) and some academic journals in Britain. The Oxford spelling uses the serial comma, which therefore is also called the Oxford comma.