I used to have the same setup. Here's what I came up with for choices:
1. L/R from VGA cable into an audio receiver. This option can be used to play sound through either speakers or headphones. Extension RCA cable probably needed though. When playing sound through headphones, using the mic is a problem. You could purchase gaming headphones with attached mic.
2. L/R from VGA cable into an RCA (L/R, female) to 1/4" or 1/8" stereo (female) Y-adapter. Attach headphones, adjust sound using in-game options. The major problem with this setup is using the mic. I bought a pair of gaming headphones with an attached mic.
you can get a phono (phono is red and white RCA for audio) to female 3.5mm cable as above and then get a 2.5mm to 3.5mm female to plug in your gamepad for the mic.
Or you can use a set of old PC speakers, or alternatively, use the phono to connect to the back of a stereo system in the AUX and that works too.
The headphones work, but the volume ain't the best and you dont have complete control over it. I went with a diff option altogether and used the optical out to a 5.1 system, but I tried the others first.
The gaming headset you posted looks great, but it won't work with the Xbox without an additional adapter. Since manufacturers have to license their products with M$, your choices for gaming headsets are limited. I purchased a Turtle Beach headset that works with both the PC and Xbox. Here's a link to the newer version of my headset:
Plugging the Xbox directly into your speakers should work fine if your subwoofer takes a L/R RCA audio in. The Logitech site has the X-540 which has a gaming console adapter--I couldn't find any info on the inputs of your system.
If listening through headphones is fine with you, then my advice is to go buy a good gaming headset. If you're going to use the headset with a PC, then find a headset that works with both the PC and Xbox.