Hair and Makeup is primarily a female aspect to headshots. But men, always bring translucent powder, shine blotting paper and cherry Chapstick. The cherry Chapstick is brand specific. It has a slight amount of color and no shine so you don't look like you are wearing lipgloss or lip stick but handles the ashiness or colorless thing that often happens for mens photoshoots. This is such an important tool for men that I tell every male client I have to always use that before a photoshoot and before an audition. When you go into an audition casting usually records your audition. Its one small thing to help you for camera gentlemen. For men with skin issues, you should look into hiring a makeup artist for your shoot.
For women make up and hair is a part of headshots decisions you need to make and weight out with your budget. It can dramatically increase your cost, but it can be worth it. Most women know the range of makeup needed for their headshots. You aren't doing crazy makeup. You start off fresh clean and simple and work your way to more dramatic, if that is a part of your casting. But it takes energy and rushes you personally in the photoshoot. About half my clients come with their clean fresh faced light makeup and they personally build up through their casting. The other half hire professional makeup artist. When you are doing that you should arrive fresh faced giving your makeup artist a clean slate.
Most people who are hiring a makeup artist will strive to find someone that does both hair and makeup and can extend the length of time of your shoot. Even if you are hiring a hair stylist or a makeup artist that can do hair, you need to arrive with your hair ready for the first look. This saves massive time. But if you can afford both hair and makeup, I do recommend doing both because it saves you time and allows for more shots to be taken.