For horror, Stephen King is one of the best. Start with something shorter of his, a short novel, or one of his collections of short stories. His longer novels are great too, but his short stories are where he really shines.

A couple of my favourites are:

1408

The man in the black suit

Pet Cemetery

The raft.

The cycle of the werewolf.

Happy reading!

Edit: for mystery I enjoyed Six Wakes by Muir Lafferty, a SciFi murder mystery on a spaceship. I also enjoyed Agatha Christie's Hercule Poirot stories, they're fairly simple and easy to read.