What animes would you recommend me?

Dennou Coil is a really underappreciated anime. It's one of the best anime I've ever seen, and I don't know why more people haven't watched it. The first part is lighthearted and a little funny while building up the world around it and giving you important information, and the second part just delves into the chilling mystery of the truth behind the cyber world and hooks you to the screen until you finish it. I think this is exactly what you're looking for, as the show has a depressing background, the first part is lighthearted comedy/adventure, and the second part is a suspenseful mystery.