and

Don’t hesitate to start a sentence with And. It’s a coordinating conjunction, and great writers have been starting sentences with conjunctions for hundreds of years. You can remember the coordinating conjunctions by referring to the acronym BOYFANS: but, or, yet, for, and, nor, so. You can begin a sentence with any of these. And you should.

Here’s Justice Oliver Wendell Holmes:

Courts proceed step by step. And we now have to consider whether the cautious statement in the former case marked the limit of the law . . . . Johnson v. United States, 228 U.S. 457, 458 (1913).

You'll find a thorough discussion of coordinating conjunctions in the Parts of Speech section of Grammar.com. Click here for the beginning of that discussion.