As you can probably guess from my username, I will recommend that you read the Lovecraft book first. Despite his peculiar style and relatively small body of work his influence on modern horror is almost impossible to overstate. Start with
The Call of Cthulhu, The Colour Out of Space, The Shadow Over Innsmouth, At the Mountains of Madness, and
The Case of Charles Dexter Ward. HPL's work recently came into the public domain, it can be read in full
here along with a lot of other interesting material.
Older authors: Edgar Allan Poe, Algernon Blackwood, William Hope Hodgson, and Arthur Machen (mainly
The Great God Pan).
My favorite living horror author (indeed, favorite living author) is Dan Simmons. He has written almost all kinds of fiction but even his SF and historical fiction has plenty of horror elements, he's not shy about doing horrible things to his characters.
Summer Of Night is incredible, it's similar to King's
It but better in every conceivable way. Its sequel
A Winter Haunting and psuedosequel
Children Of Night are somewhat lesser but are still extremely good. His short story collection
Prayers To Broken Stones is also excellent.