The really great stuff in TrekLit is the big interconnected continuity taking place after all the shows are over. The link in my signature is a big flowchart of all of it, and nearly every book on that chart is certified awesome.
If you're looking for some standalones to read during the shows, since you like Q,
http://memory-beta.wikia.com/wiki/Q go here (don't read the article just scroll down), go down to "Appearances", and any TNG book in that list is gonna be pretty great. The Peter David ones, "Q-In-Law", "Q Squared", and "I, Q" are all fantastic, for instance.
The best Klingon Empire stuff takes place after DS9 is over, and is in the top right on my fantastic flowchart.
But one last recommendation - Vanguard is a series that takes place alongside The Original Series but involves mostly original characters on a space station in a totally original storyline. It's absolutely freaking outstanding, ungodly awesome, even if you're not too hot on TOS. It's one of TrekLit's very best series, and you can read it without finishing any of the 24th century shows. That's where I'd start. (The list of titles is in the bottom left of the flowchart.)