Science Ninja Team Gatchaman (gotta love that laundry-list of a title) is the “gateway anime” for many people. I never saw it. But I appreciate the appeal. Teenagers who are ninjas superheroes in space–who also rode motorcycles? I think they also rode motorcycles–are one-stop-shopping for all your entertainment needs. Add the fact that they are dressed as animals, and well, it doesn’t matter what you’re into, does it? Science Ninja Team Gatchaman has what you’re looking for.
My gateway technically was Voltron and ThunderCats, but I didn’t register them as “anime” at the tme, and have next to no memory of them. I remember putting on a episode of Voltron on as teenager when I worked at a video store, and being thunderstruck that mice were characters. My childhood brain had nixed the mice completely, preferring to focus on the mechanical lions that turned into a giant robot. There’s the charm of the everything-at-once school of entertainment; whatever you don’t like, you can compartmentalize away.