I feel as though the AmE vs. BrE distinction is largely exaggerated by
non-native English speakers. In reality, the language itself is 99% the
same (the only real differences are pronunciation and a few minor
variations in spelling); and the vast majority of the time, English
speakers from different countries have no difficulty understanding each
other. Consequently, I think that attempting to "learn" one instead of
the other is largely a pointless excercise, as most non-native
speakers are unable to closely emulate the pronunciation and speech pattern to the point that a native speaker would be able to differentiate between someone that supposedly learned AmE rather than BrE. The person speaking would simply be thought of as "a person of country/language X that is speaking English."
Like a previous poster commented, your focus should be on using proper grammar and working to improve your pronunciation rather than worrying about the
minor differences in the usage of language between two countries.