I can co-sign on what Brine is saying here… lots of bang for the buck with computer speakers. I had some logitech speakers that sounded great and had a sub too.
If you go with smaller monitor speakers with 5" cones they just don’t move enough air without a sub.
Honestly it really depends on how you’re mixing as well I think. I spend much more of my time listening in my HDJ-2000’s than I do to any external source at home, and that’s just how I’ve gotten used to it. A combination of having to play quietly at times late at night, and done a couple little house parties without a proper monitor. Mixing is almost all in the cans, and then I take them off to adjust as needed.
So for “in the bedroom” sound, I don’t really need a perfectly crisp sound, as long as it covers all of the frequencies I want to a decent degree. I’m also someone who likes a muddy system with a sub over a perfectly crisp system with no bass, so go figure.
I bought my Logitech 5.1 surround sound system in 2003. And it is still killing it. Not many pieces of technology that I’ve had last this long 
I didin’t say you could get good speakers and a sub for $600. I said that if you have $600 you’d be better off buying a hifi system (seperates) rather than buying active monitors. This is partly due to the fact that the advantages of active monitors only really come into play when money is no longer a real issue (have a look on gearslutz.com for detailed explanations of this).
My recomendation would probably be to get a nicam amp and some second hand B&W speakers.