I don't buy into the rule that says you should never begin a sentence with the word 'but'. If the preceding clause is complex, starting a fresh sentence often increases readability. That said, there are principles you should remember when using 'however' as an alternative.
Picture by Frank Micelotta/Getty Images
Mind Your Language's oracle on these matters, the Macquarie Dictionary, offers useful advice on both these points. Here it is on 'but' at the start of sentences:
Some writers object to sentences beginning with but on the grounds that it is a conjunction which should link clauses within a sentence and should not appear to link a new sentence with the previous one. In fact many writers do use but at the beginning of a sentence and there is no reason to object to the practice provided that it is not overdone.
Writers who don't favour using 'but' in this way often turn to 'however' as an alternative. That can be a useful strategy, and a way of introducing variety. However, there are pitfalls here too, as the Macquarie points out:
It is now common to begin a sentence with However, but it should be noted that a comma after it may be useful in distinguishing however meaninging 'nevertheless' from however meaning 'in whatever way'.
You can see that clearly with these sentence beginnings:
However, the writer chose a different approach . . .
However the writer chose a different approach . . .
The first conveys the sense "despite what we have discussed previously, the writer chose a different approach". The second conveys the sense "We don't know how the writer chose a different approach". Adding the comma after 'however' makes that distinction much clearer, even without knowing how the sentences end.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.