The Corsair SP2500 is a crossover between music speakers and gaming speakers but, for the sound you get, they are reasonably compact, especially since they do not need an extra DAC and tuner/amplifiers cluttering up space. The sub is fairly huge but will easily fit in the knee hole of pretty much all desks, except maybe one designed for a preschooler.
Most audiophiles (the ones I call insufferable audio snobs) turn up their noses at the SP2500 because it doesn't follow the traditional rules of what most audio snobs audiophiles to consider necessary for high quality equipment. While the SP2500 does make some drastic compromises to get quality sound from a comparatively small set of speakers (such as raising the crossover between bass and midrange to compensate for the 3" midrange speakers and letting the sub take up the slack for the lower end of the midrange), the sound is surprisingly good. The speakers are actually limited to a degree to the quality of sound all but possibly the very newest, high end motherboards can produce. They usually can benefit from having a high end sound card in the computer. But, even without a good soundcard, these speakers still sound surprisingly good.
One of the two biggest disadvantages of the SP2500 is the price. I suggest trying to catch them when they are on sale. You shouldn't spend more than $220 for them, preferably around $200-$210 (I found mine around 2.5 years ago for only $190). I also suggest staying away used ones since some of the earlier ones had some problems; the current new ones will be ok.
The other big disadvantage of the SP2500 is also one of its advantages: it has a lot of settings in its control pod and onscreen in the driver. You do have to spend a lot of time fiddling with the settings to get the speakers dialed in for thee room they are used in and your personal tastes. One tip: the sub may seem to be too quiet when you first fire it up. Don't be afraid to crank the volume up to what you consider to be a reasonable level. While you can get thundering bass that is guaranteed to anger your neighbors, I don't recommend it if you want the speakers to last for a while. I keep my sub set to normal levels, the kind you have for listening to classical music and it's still in the upper end of the volume range (although cranking it all the way up would still rattle the windows and my fillings).
I've been very happy with my SP2500s. I didn't recommend them to you because they were out of your price range and they are generally a bit overkill for use with onboard computer sound. But, as AddRam said, if you can stand to up your budget (and/or can catch them on sale), you may find you will like them. Again, try to buy them locally somewhere that will allow you to return them should you not like them.
I also have an ASUS Xonar Essence STX sound card. I paid more for it locally than it would have cost me online but that gave me more time to fiddle with the settings on it and the SP2500 and still be able to return it should I find it didn't improve the sound enough to be worth the cost (it was well worth it, in my not so humble opinion, but you may or may not agree). The original STX has now been replaced with two versions of the Xonar Essence STX II. One is strictly 2.0 or 2.1 and the other includes a daughter board for 5.1 and 7.1. For music, anything more than 2.1 is overkill. for movies and gaming, 5.1 or 7.1 may be worthwhile but the price is much higher. In any event, a sound card is something you can do without or put off until you can afford it and still enjoy your speakers.
