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, though you should be warned that there are a number of Safety Notifications and / or warnings specific to to each of the sports of Hang Gliding and Paragliding which have been published about this "pointy end" style.)
Helmet Manufacturers List