technically you have three options..
logitch z906 or z5500
-this can take either 3.5mm or optical spdif for sound. it will work great for any device with optical output (pc, game systems, any decent blueray player) but i'm not sure what your cable box outputs as.. if component you could probably use an adapter cable to use the 3.5mm ports. you could likely get it working fine but its not going to be as easy as a receiver option.
logitech z906 $294 (new model which replaces the z5500, good but not quite as good as the previous)
http/www.amazon.com/Logitech-Surround-Speaker-System-980-000467/dp/B004M18O60/ref=sr_1_1?ie=UTF8&qid=1380802668&sr=8-1&keywords=logitech+z906
logitech z5500 $600 (because of popularity... its considered the best set for computer speakers)
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receiver+speakers+sub
-a receiver really gives alot of options and is the easiest to connect up and switch both your audio and video inputs at once however it is not a cheap option. unless you buy something really shoddy (HTiB sets or just bad speakers), used (can get some good deals), or lower down to a 2.1 or 3.1 to start (to save cash) its going to be hard to do it for $600. i said hard... but not impossible. there are a few diamonds in the rough to be found as i listed below.
energy take classic 5.1 $350
amazon:
http/www.amazon.com/Energy-Classic-Theater-System-Black/dp/B001202C44
review:
http/reviews.cnet.com/surround-speaker-systems/energy-take-classic-5/4505-7868_7-33310963.html
yamaha 5.1 receiver $360
http/www.amazon.com/Yamaha-HTR-4065BL-5-1-Channel-575-Watt-Receiver/dp/B00963S6TE/ref=sr_1_4?s=aht&ie=UTF8&qid=1380802568&sr=1-4
of couse you could go with a cheaper receiver or a different brand. personally i like pioneer but i've heard onkyo is "alright" for low end. i've heard to avoid budget sony receivers.
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computer speakers+switch+adapter cables
anything from logitech generally isnt terrible. you would need a switch which works with all of your devices and can output component audio that you would have to adapt to 3.5mm with cables. honestly its messy and not a very nice solution. its probably the cheapest solution however. i would say you could spend $200 for everything.
definitely not ideal. swapping sources wouldnt be much of a problem but you will have lots and lots and lots of wires and with all of the switching and adapter cables required sound quality might start to get affected.
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my recommendations?
i would say receiver+ht speakers or possibly z906/z5500 as a second choice. you might want to look on ebay as well for good deals (i only quick searched amazon)