I have read some sources say you never start a sentence with a conjunction, other sources say it is acceptable. and in some cases better. So can you start a sentence with the word "But" and if so, when is it acceptable?
From the Chicago Manual of Style:
There is a widespread belief—one with no historical or grammatical foundation—that it is an error to begin a sentence with a conjunction such as 'and', 'but', or 'so'. In fact, a substantial percentage (often as many as 10 percent) of the sentences in first-rate writing begin with conjunctions. It has been so for centuries, and even the most conservative grammarians have followed this practice.
But only do this for emphasis. And not all the time. So it doesn't get old.
Sticking to the technical grammar definition, a conjunction is a word that connects two phrases within the same sentence. If you start a sentence with a conjunction, one of the phrases is in a different sentence. Therefore the conjunction is uneeded, and it is improper grammar to begin a sentence with one.
HOWEVER: do not let the rules of grammar hinder your writing. Let them help it only.
Plenty of writers will start a sentence with a conjunction, as well as do a multitude of other 'grammatically incorrect' things. They can do this because it comes down to writer preference. If you feel you can get across what you are trying to say if you deviate from the rules of grammar, do it. If not, then don't. Point in case. I used a double negative in that last sentence. The word 'uneeded' above is actually not a word at all.
The question of whether you should start a sentence with a conjunction is entirely up to you, and how you think it sounds. I've found it to be fine within a chapter. When it gets jarring for me is when a chapter is begun with a conjunction. However, you might not feel this way. It's writer preference; do whatever sounds best to you.