Use whatever chili powder you can get your hands on. I’ve made it with ancho chili powder, guajillo, and New Mexico chili powder and a blend of all 3 and they all turned out fine. My favorite was probably the NM chili powder, though.
The type of cheese is up to you. Some people love and are accustomed to American cheese enchiladas and that is just fine. I prefer a mild or medium yellow cheddar but Monterey Jack is good, too!