Not in this State of SC, NK.
for handguns ... You must be 21 years old, a non-felon, you must have a background check ( ie. 5 day wait) unless you possess a CCW/CWP.
For rifles and shotguns the age is 19 I think, and fill out proper paperwork, been so long since i bought a rifle I don't know if they do a background check for a rifle or not. They used to not.
The only thing class wise mandatory at this point is any hunter born after 1986 must attend Hunter's Ed a class mostly on state laws and hunting morals to obtain hunting permit.