The JBL Cinema is not a self-powered speaker system. Only the subwoofer contains a power amplifier, the other 5 speakers must be driven by an external amplifier. You will need a 5.1 channel power amplifier such as this Denon receiver at about $200.
An AV receiver does much more than you would need - it accepts and switches multiple inputs both audio and video, has an AM/FM tuner, etc., but these are actually more common and cheaper than a device that has only the power amplifier. Those tend to be very much higher quality and more expensive.
A much easier and more popular choice would be to buy a 5.1 speaker system that is designed specifically for use with a computer - the main difference being that these have their own internal power amplifiers and will connect directly to your PC. Here's the top of the line Logitech 5.1 system at Newegg for $330.
I get that you want to go "high end" and you believed the JBL would be better than "PC speakers" and that might be true, but a high quality system designed specifically for PC use may give a better result, easier use and integration, and lower cost.
CNet reviewers make the case that a very high quality 2 channel system is a better choice for desktop use. I have owned music systems costing many thousands of dollars for decades, but for all day use working at my desk (I'm a programmer) I use a pair of M-Audio speakers and am very happy with their excellent sound!