IMO, you cannot go wrong with King's short story collections. Fave book, The Stand...which has horror, but not strictly. IT is a fine place to start...just, enjoy the voyage, if not the ending.
Outside of that, Lansdale, Joe R.R. is a fine writer. If you can find them cheap Book of the Dead 1 & 2 are 2 of the finest Zombie anthologies ever. Which leads to Skipp/Spector, who wrote some TREMENDOUS books together, the Bridge/Animal/The Scream...Robert McCammon USED to write great stuff too. Richard Laymon, Dan Simmons, Jack Ketchum, F. Paul Wilson, all some good writers too. Best advice I can give, pick up anthologies, lots of em. You will be sure to find a writer you take a fancy to and then it's a matter of checking his/her past work out.