Top 3 I'd recommend if you want a good starting package:
1. Code Geass (Thriller drama with action, my all time favorite)
2. Steins;Gate (Thriller)
3. Boku No Hero Academia (More noob friendly and good introduction to Shounens(think dragonball, naruto, bleach, etc basically shows that can go on forever), good if you love intense and meaningful fights)
Best movies if you want to waste a hour or two:
1. The Fake (another thriller with lots of drama and a twisted ending if you can withstand the animation quality the story will quickly make it up to you and become one of your favorites)
2. 5 CM per second (romance movie with reality actually being a factor in this movie)
3. Spirited away (classic)