Starting sentences with But (and other conjunctions)
In spite of what you probably learned, starting sentences with But and other conjunctions is grammatically acceptable and often effective. See the following authorities:
Dictionary of Modern American Useage, page 99 of the first edition.
Chicago Manual of Style, 5.191, page 193 of the 15th edition.
Style: Ten Lesson in Clarity and Grace, page 17 of the 8th edition.
To understand why an opening But is often effective at quickly changing the argument or flow, see However.
Note that the opening But should not be followed by a comma unless a parenthetical clause or phrase immediately follows. The comma should be avoided because the purpose of the But is to get the sentence going quickly, and the comma slows it down.
But at the start can cause problems. Consider my recent experience. I submitted a research paper containing eight or so sentences starting with But and no following commas. Neither the reviewers nor the Editor commented on this, but when I received the proofs, the Technical Editor had changed all my Buts to 'Howevers,'. I requested that these by changed back to But, and they did that but left the commas in. As a result, I now consider this my BUT COMMA publication because I cannot look at it without seeing 'But,' everywhere, and so I cannot look at it at all.