As far as SF goes, I would definitely start at the local library and see which authors you like best. For me, the off the top of my head list is: Asimov, Greg Bear, David Brin, Benford, Arthur C Clarke, Samuel Delaney, Eando Binder, James Tiptree, Jr., Harlan Ellison, Frederick Pohl, Poul Anderson, CJ Cherryh, Ursula K LeGuin, Robert Silverberg, Robert Bloch, Robert A Heinlein, Roger Zelazney, Larry Niven, Stephen Barnes, Joanna Russ, Suzy McKee Charnas (some of the best vampire stories I've ever read).

You could also look for anthologies called "The Year's Best SF" for $Year to get a good sampling of a lot of authors. There's also a multi-volume set "The Best SF of all time" and any Hugo or Nebula Award winner compilations are going to contain the "good stuff". (Hugo awards are voted by the SF fandom communiuty, Nebulas by members of the SF Writers of America - I don't know what the British equivilent is for that).