Once you begin soaring flight, you'll need a parachute. It's extremely unlikely that you'll ever deploy it, but it's better to have one and not need it, than to need one and not have it. Regardless, most sites will require you to have one.
In the United States, there are three current designs that are popular. Free Flight Enterprises makes two designs, the Pulled Down Apex (PDA) and the Low Aspect Ratio Annular (LARA). Both are distributed by Wills Wing. High Energy Sports is the other principal U. S. maker of hang glider reserve parachutes. Their current product is the Quantum Series. High Energy Sports offers parachute clinics around the country. These are superior safety training events for pilots, and cover much more than the repack (which is included in the clinic). When you have the opportunity, participate in one of these clinics.
Because the pilot does not cut away from his glider when deploying, there is a chance that the glider may be spinning while descending. Because of this, you will want your parachute to be equipped with a paraswivel. This will keep the spinning glider from twisting the parachute lines and possibly collapsing the canopy.
Parachutes should be repacked every six months by someone who has been trained in the repacking techniques of low speed emergency parachutes. Because hang glider pilots do not cut away from the glider when deploying the emergency parachute, they are descending at a much lower rate than would a skydiver would be, so the parachute is of a different design than is a skydiver's reserve parachute. Accordingly, not all parachute riggers are qualified to repack a hang glider's emergency parachute.
Quality used parachutes can be hard to come by, so expect to buy this new.