I would recommend anthology horror movies. There is always a variety of stories in them. So they can get an idea if they like gore, darker horror, comedic horror, etc. I would recommend
Tales From The Darkside: The Movie
Tales Of Terror
Tales From The Hood
Trick R Treat
V/H/S and V/H/S 2
I feel the V/H/S films are vastly under appreciated. Definite must for a new horror fan.