An “And” or a “But” (or a “For” or an “Or” or a “However” or a “Because,” to cite four other sentence starters one is often warned against) is not always the strongest beginning for a sentence, and making a relentless habit of using any of them palls quickly. You may find that you don’t need that “And” at all. You may find that your “And” or “But” sentence might easily attach to its predecessor sentence with either a comma or a semicolon.