Recommendations I'd second:
Dresden files starting with storm front.
Enders Game.
Altered Carbon.
Scar Night(though the sequels aren't as good. It's a good book, but not incredible, imo).
Terry Pratchetts Discworld Novels.
The Prince of Nothing Trilogy by R Scott bakker(starting with The Darkness that comes before).
I'd also recommend these authors, in SF terms:
China Mieville. Particularly his New Crobuzon novels, beginning with Perdido Street Station.
Steven Eriksons Malazan Books of the Fallen, starting with Gardens of the Moon(probably the weakest of the series-best to persevere)
Frank Herberts Dune.
Glen Cooks Black Company books(starting with "The black company"-can buy the first few as an omnibus).
Alastair Reynolds Revelation Space series.
Scott Lynch-The Lies of Locke Lamora.
Most books by Guy Gavriel Kay. Maybe Lions of Al-Rassan to start.
As well as these, a lot of books commonly held as classics are worth reading. Though, particularly with the much older stuff like Dickens or Austen, I'd advise you read a bit before buying. Some people find the prose rather off-putting.
Personally, I wouldn't bother with 1984, if you're just looking for a story. Orwell was an essayist, and it kind of shows at times. I also felt the book was a bit unsubtle. Orwell also seems to sacrfice the plot in order to get his point across. It's got some great concepts, and is certainly an interesting read, but if you're looking for a story, it's probably not the best thing you could choose.
In the line of the classics, I'd recommend Heart of Darkness by Conrad most strongly.