Well, I've had the SR-225s for a couple months now, and I just got the HD600 a couple days ago.
I like the HD600 better on most recordings. It's smoother, has deeper bass and is about 800% more comfortable than the Grados. In fact, they are actually pleasant to wear!
However, I don't think they will be driven well by a soundcard. With the 300 ohm impedance, they require relatively high voltage to drive. (but relatively low current) The sound card will have the current, but not the voltage. Sound cards are limited by a 5V single sided power supply. Not to mention that it has to share that supply with a noisy computer!
As for the 580 vs 600, I don't know. I haven't heard the 580. But if it's really 95% of the 600 like people say then you'll just have to judge if that's important to you. I know if I were on a budget, the 580 would be a no-brainer!
If your MP3s are of high enough quality and bitrate, they should be virtually indististinguishable from the CDs, so if you can hear a difference between the 580 and 600, I think you'll hear it with MP3s as well.
I haven't tried my 600s in my SBLive card, but the Grados sound pretty good through the line output. They do seem to have a bit of distortion, but it was better than I expected. Maybe the TB is better.
Highly recommend an amp with either of these! Alternatively, if you can find an old receiver, some of them have decent headphone amps built in.