You'll learn faster. You should visit several DZs in your area on a weekend when the weather is good. A couple of hours at a DZ and a few short conversations with some of the people there will give you a better idea which one feels right for you. A. Several DZs occasionally offer high altitude jumps, usually from altitudes of about 20,000 feet. For skydives at those altitudes, jumpers need oxygen in the aircraft but not in freefall, providing they breathe oxygen until immediately before exit.
Training is required, but it's quick and easy.
Instructors rated by the U.S. Parachute Association can provide basic instruction on such jumps. For jumps higher than 20,000 feet, skydivers need better training and special equipment. The one-day course includes a ride in an altitude chamber, so you learn more about your body's reactions to higher altitudes. It's a good course, and it's essentially free. Other than that, the FAA doesn't play a role in high-altitude parachute jumps.