I honestly don't game very much and when I do I don't need to hear footsteps coming in X direction, etc.  My price range is up to 600$ or so.
I'll be using these mostly to listen to music, no specific genre really.
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• Stereo Link USB sound card (~$100) The sound card should have a good DAC. This is where the signal is converted from digital to analog. You can get a decent stereo PCI sound card for a bit less. But I got a USB based one because of multi-OS support (no need for drivers). It also should be affected less by interference theoretically. It's a good idea to buy a sound card with a DAC supporting high resolution and sampling rate like 24bit/96kHz. But generally the difference is considered inaudible. So get the sound card which has a solid reputation of quality even if it is 16 bit. Also if you want no recording abilities, get one with none or very basic recording capability. More circuitry for unneccessary components means you effectively pay less and thus get less for the components you'll be using (my motto for hi-fi system construction).
• AudioSource Amp Two amplifier (~$200 refurbished) An amplifier is a device that drives the speakers by amplifying the analog signal to a level that is sufficent. This is necessary because the signal coming out of your sound card is not strong enough to drive the real speakers. The ordinary computer speakers usually are not generally designed for high quality music listening so they come with their own built -in low quality amplifiers. Also I'd prefer amplifier over a receiver because the money you pay goes in the amplification circuitry rather than be wasted unnecessarily (for me) on circuitry like the FM tuner etc.
• A pair of Infinity Alpha 40 Speakers (~$550) The speakers are the most crucial element to sound quality in the chain. For this you need to read a bit of reviews and/or go to a local hi-fi store and test. Considering how much a good speaker costs, I'd recommend not to try building a 5 speaker system for your price range. You'll just be compromising from the speaker quality otherwise. I live in US and so I prefer a good brand for which I could get the most discount online. For instance my speakers used to sell for $1000 a pair when I paid $550 for a brand new+warranties from Sound Distibutors after a bit of email haggling. Know how much they sell for before you negotiate a price.
• Cables from KnuKonceptz (~$20).