Use either one. Just try to be consistent. Remember that there are quite a few more differences between American and British English than the accent; spelling, vocabulary, idioms, phrases, etc.
Nowadays more people are exposed to the American English, mainly because of the movies and entertainment. And most importantly because of business and technology.
As above, there is more than one British accent - what I think you are referring to is Received Pronunciation. It is true that most British accents do not have /r/ prounounced after a vowel, but your suggested pronciations of <word> and <forward> are not what I would say were typical. <Word> has the same vowel as girl, curl, burn, not like card, and <forward> doesn't have a strong vowel sound in the second syllable, more sort of "forewuhd".