So, to dip your toes in to anime that doesn't have crazy powers or get too weird (lots of bizarre shit in anime worlds, including the two I previously recommended, despite how incredible they are) or anything like that, the anie starter pack I always recommend are Cowboy Bebop (if you like more sci-fi) and Samurai Champloo (if you like more classic samurai). They are by the same creator and neither have anything too fantastical. Both have incredible characters and music.

I'm in my thirties, but grew up a military brat and fell in love with anime/manga as a kid when my dad was stationed in Japan. It still beats so much content that gets put out on TV today.