Oh, big sigh. Good writers have been using and and but to begin sentences since Old English. (Just take a gander at how many sentences begin with and in the King James version of the Bible (starting with Genesis)....
Thirty-eight of them begin with the word and.
I've always thought that particles like this were a kind of punctuation in non-metrical oral literature. Beginning a sentence with and or but indicates that one sentences has stopped: sort of a rhetorical version of a period (or full stop).
In translations of the bible it is simply reflecting the cadence and flow and structure of the original languages and/or authors. This is particularly true of the King James version, whose authors actually changed some of the grammatical habits of English usage by ignoring English grammar in favour of an over-literal rendering of the Hebrew, Aramaic or Greek of the Old and New Testaments.
As far as 'And' goes, this is especially true of Mark's Gospel. The KJV's formulaic translation of Mark's
kai egeneto is the familiar "And it came to pass...". Greek often starts sentences with kai, and Mark even more than your average Greek writer. Mark's favourite expression seems to be
kai euthus, which is usually translated "And immediately..."
As zmjezhd notes, in cases like this 'And' at the start of a sentence is almost a kind of punctuation mark - and not just in 'oral literature' - remember that originally uncial manuscripts had no punctuation marks or spaces between words, so this was more necessary than later when those things were invented.
