Hi
I might be repeating someone, if I do sorry.
Ok who are the big names in Sci-fi and fantasy? Some great books are listed but let me give you my personal favourites.
First is Raimond E. Feist, he writes a very good story and his stories are epic. His first series (Magicial, Silvethorn and Drakness at Sethanon) are renowened. His colaboration with Janny Wurts (Daughter of the Empire, Servant of the Empire and Mistress of the Empire) is probably my favourite fantasy series ever, politics and intrigue!
For Sci-Fi Anne McCaffrey (hope I spelled that right) is a big name. Everyone raves over her Pern series (numerous books) but I love her Rowan series (Rowan, Damia, Damia's children....I forget the rest)
David Gemmel is a fantastic fantasy writer, his books can be read individually, although they do follow on each other, I would suggest his Rigante series or his Drenai books.
After you have read some fantasy pick up a book by Terry Pratchet if you haven't already. You will either love him of loath him.
Hope this helps