The one that comes on your motherboard. Audio is limited by the speakers, not the computer. Audio is easily manipulated digitally now. There is no reason to put a physical sound card in. Especially since anything you plug into your computer is self driven (does not require more power)
I have to disagree. Onboard audio has become quite decent these days, but it still has a lower SNR and higher harmonic distortion than a dedicated audio processor will. Heck, there are a a lot of headphones out there with impedance high enough that they aren't even usable with the onboard IC at all. I don't understand what you mean by 'self-driven' - the problem isn't getting more power to the headphones, but a cleaner signal. No amount of digital modification is going to make up for a poorly-performing analog output section.
I have a pair of ATH-M50S's myself - they're the model that came before the M50X. They're great, aren't they? I wore them 'till the pleather starting falling apart and bought myself a pair of Shure SRH-940s as a replacement... everything I've owned has been run on an outboard DAC/Amplifier combo, and I can say it
does make a noticeable difference, although that being said there is one important thing that needs noted. The amount of improvement you'll get for your money from buying a sound card or DAC/amp is going to be much, much smaller than if you were to upgrade the headphones themselves. The M50s are an amazing value for the money, but $150 is still a reasonable distance below the point of diminishing returns, and I don't feel that you'd get a worthwhile improvement in sound quality from running them on a $50 sound card I'm not telling you to go replace your M50s - I'm just trying to say that you shouldn't expect to hear a significant difference from your current setup.
If you
do want a new source for your headphones, I'd have to recommend saving a bit more and purchasing an outboard DAC. It would serve you much better in the future if you decide to upgrade - they can be used with any system, sound noticeable cleaner, and would be a great platform for more expensive cans. Having an internal sound card would be a small improvement, but the problem of EMI from within your computer is still there... this is helped immensely by physically moving your audio outside of the PC case. FIIO makes the E09K for $100 right now which is a nice unit for the money, and I'm sure there are quite a few others around the $100 price point. If you want a whole boatload of options thrown at you, try asking this same question over at the Head-Fi Forums, too!
Just my opinion - take it for what it's worth!
