This is a fun bit of trivia I wish I could go back and show my high school English teacher: according to the Chicago Manual of Style 5.206, it’s okay to begin a sentence with a conjunction. A conjunction is a joiner, typically of two sentences or thoughts—and, but, however, therefore, etc.
The CMoS authors claim that as many as 10 percent of sentences in first-rate writing begin with a conjunction. I feel so vindicated.
CMoS does caution to test the word to see if it is really needed. In the case of “but,” can the word “and” be substituted for it? If so, it’s the wrong word or it isn’t needed at all.
I walked to work today. But I left my briefcase on the table.
In this case, the conjunction should be “and” because they are not two opposing thoughts.
And it should be one sentence. Starting with a conjunction is usually done for emphasis.
Don’t go crazy with this new-found power of starting a sentence with a conjunction, but feel free to use it to change things up and vary your sentence structures.