man/men....
That's true, this is simpler if you aim for an American pronunciation. Some grammar is marginally easier in American English too.
But as I said before, Russian people sound chic and sophisticated when they speak with a more British accent. Less so with an American accent.... IMHO.... !

True, the sparrow probably wasn't a very good example -- I doubt any ESL teacher would include "sparrow" on a vocabulary list for students below the advanced level. (Whereas words like "chicken", "pigeon", and "parrot" might be introduced even in a beginning class, although after the generic term "bird".)
Everyone knows how rubbish I am at Russian, and un-talented (beginning to sink in when I compare myself with my colleague that I mentioned earlier...) I am just an advanced beginner. But I can actually name lots of birds in Russian. Swallow, parrot, stork, swan, chicken and pidgeon. Maybe some more that I am forgetting. Russian people have a thing for singing about birds, I think... ! That's why I know so many birds names...