Raymond Chandler’s the king of crime fiction for me, so you should definitely read a couple of his Philip Marlowe novels. The plots are incredibly convoluted, but you don’t really read Chandler novels for the plot anyway. Read him instead for the down-at-heel nobility of Marlowe and Chandler’s own superb phrase-making.
Ian Rankin’s not bad, and his Inspector Rebus novels are worth trying too. They conjure up the darker side of Edinburgh pretty well, and Rebus himself is cantankerous enough to make an entertaining guide.
The Sherlock Holmes short stories are great too, of course, so you should certainly give them a try. They’re wonderfully well-written, very evocative of Victorian London and unsurpassed in the creation of Holmes himself. Stick to the short stories though: they’re really the core of the Holmes canon.
George V Higgins is another favourite of mine. He writes about small-time crooks in Boston, reveling in their stupidity and telling the story mostly through well-observed and very colourful dialogue. He’s one of the few crime writers who can incorporate so much humour into his stories without tipping them over into outright farce.
Carl Hiassen’s Florida-set crime novels have a lot of humour in them too, though in his case it’s aimed at satirising crooked Florida politicians and greedy developers. Two or three of his novels were enough for me, but many other people swear by him.
Finally, you might want to try James Lee Burke and his Dave Robicheaux series. They’re set in Louisiana, with a very strong sense of place, some nicely lyrical writing and a string of satisfyingly sadistic villains. Two or three books in, you start to realise that they’re all written to the same basic formula, but by then you might have developed enough affection for the characters to keep going anyway.
All these guys are easy to read, and provide very accomplished page-turners. Beyond that, it’s really a case of whether you prefer a British of a US setting and how down-and-dirty you want to get with the violence and corruption involved in their plots.
As for true crime, David Simon’s Homicide: A Year on the Killing Streets and The Corner are now both available as paperbacks here in the UK. They’ll give you a very good street-level view of Baltimore’s drug trade and the violence it produces as, of course, will Simon’s phenomonally good HBO series The Wire.