lepai 2020a+ amplifier paired with dayton b652 speakers as featured in this article
http://www.cnet.com/news/build-your-own-desktop-stereo-... are really quite good for $70. sure, it might be a low end amplifier however it will work for this situation and you wont get any better without dishing out quite a bit more cash. the speakers are excellent for the money and compare with speakers twice their value favorably.
it will blow away the z313 and likely even the z623. the only thing the logitech sets will have is more bass... and for that you could add a $109 dayton sub-1000 which is a 100w subwoofer to pair up with those daytons and have yourself a party. certainly a good option if you wanted hifi on a budget.
...hmm actually it looks like dayton has made a kit out of them since they were so popular including their own brand of amp
http://www.parts-express.com/dayton-audio-t-amp-and-b65... though it might lack the power of the 2020 it may be worth looking into as an alternative.
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"desktop" sized speakers are satelite size. these will lack bass response and require a subwoofer to hit low. bookshelves are a bit bigger and generally more able to hit low notes without a subwoofer (though a subwoofer still helps).
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i would avoid genius speakers personally. they are junk and are "loud" but not with good "quality" to sound. i'd say they are worse than logitechs in the same price ranges.
the z313 is not bad for the price but is certainly not going to compete with anything in a higher price bracket. we have a pair and while good for the $30 you pay there are certainly better options if you have the budget for it. logitechs tend to have average sound quality and a bit more volume/bass then other sets. if you needed cheap.. they are okay.
the z523 is a step up from the 313 but still not as good in terms of audio quality as the daytons. you might get a bit more boom due to the subwoofer but if you added a subwoofer to the daytons it would blow them away.
if bass is not a concern the creative t20/t40 sets are pretty good as well
the jbl creature iii are also a respectable set of speakers for quality.
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as far as soundcards are concerned... the dg cannot really be compared with the z. instead, the z should be compared with the dx.
any of them will be able to power your 558's. i'm not sure about the z but i know the dx uses the same dac chip as the stx which is double the price.
asus cards use "dolby headphone" while creative uses "sbx" (formerly they used cmss3d). i'd recommend you youtube a few videos for comparisions to see which virtual surround you like better. if you dont care about virtual surround for games then you can ignore this point.
i've heard that drivers are easier to work with on the creative cards but i use many asus products and i dont have an issue. sorry, i dont use a soundcard so i cannot tell you specifically about their soundcard drivers.
is there a reason why you cannot plug into the front of your pc with headphones? if your front panel audio jack is bad then you could replace it. or put a front panel bay device in to give you more usb ports and front panel audio which works again.