Well, I'd say that a good starting point would be the Pan Books of Horror Stories - 30 volumes that ran from 1959 to 1989. Admittedly, the earlier volumes were better than the later ones but they're certainly worth collecting.

The Fontana Books of Ghost Stories are good too, edited by one of my favourite authors, the great Robert Aickman.

If the occult is your thing then The Mayflower Books of Black Magic Stories are good, edited by Michel Parry. I can't remember how many of those there are off the top of my head.

There are lots of fun ones too that were brought out under the names of genre stars of the day, The Boris Karloff Horror Anthology, at least a couple under Christopher Lee's name, several Hitchcock ones too.

Regards,
Nash.