You'll need a helmet. These come in two styles, open face
or full face
The choice is yours. The consensus is that a helmet with a chin bar provides more protection.
Airsports (that includes hang gliding) helmets are made to conform to a European standard (CE EN 966). A typical full face helmet will weigh around 1.5 lbs (700 g), which is considerably lighter than a motorcycle helmet.
Some pilots have chosen to wear downhill bicycling helmets or motocross helmets A downhill bicycling helmet will weigh around 2 lbs (900 g) and a motocross helmet will typically weigh 3.3 lbs (1500 g), so both will give your neck muscles more of a workout. Each will also provide more protection should that be needed.
Some really cool helmets can be found at Icaro 2000 website (including "teardrop" helmets that most competition pilots wear).