I just finished The Long Goodbye, only the second Chandler I've ever read (the first was The Big Sleep for a class) and I have to say  it knocked my socks off.  The dude can write.  I enjoy mysteries of all shapes and sizes, but am rarely struck by the prose.  With Long Goodbye, I lost count of how many times I stopped in the middle of the paragraph to think "Wow, what an ingenious way of phrasing that!"  I'm definitely hooked.  But now I'm not sure where to start?  I'm looking for Farewell My Lovely and others at the library, which ones are the best to go with from here?

I don't think you'll be disappointed no matter which you book you select next. He doesn't have a huge list. Not only is his prose excellent, but his dialogue is as well.

The Long Goodbye is freaking amazing, and IMO Chandler is one of the most underestimated writers ever.   I love, love, love him.  I agree with everything Jodi said above, but maybe try Farewell, My Lovely next.