Backdrops and shirt colors are important. If you choose a white background for your headshot and then wear a white or very light shirt you will blend into the background. Conversely if we do an outdoor shoot, with greenery in the behind you, a white shirt could be the perfect pick. Consider your background while choosing your clothes.
Tips to help you get your best headshot
I usually recommend dressing similar to what you would for an interview, or wear an outfit with a classic look. Consider your line of work. Are you an accountant or a programmer? What is the dress standard for your industry?