No soundcard will power HD650 sufficiently alone. You can gain enough volume, but that's not the point (in fact I think even an IPod can give enough volume with them). To use simple terms, amps with power untangle different instruments, tighten and separate each one of them. Lack of power results in a big mixed soup of sound. Think of it like putting a beef steak, vegetables, starter, desert all in a bender and turning them into a drink - it's all there, but not the same as having them separately.
Personally, I think HD650 is an overkill without having a good amp ($300 upward). I think the likes of
Gilmore Lite is the bear minimum if you want to get something out of those cans. Otherwise you might just as well pay less for HD580 or 600 (or lower) and you would still hear the same-ish result.
The so called digital analogue converter (DAC) is another option. They plug directly into USB and converts the signal into analogue which headphones/speakers can understand. That way you can bypass the crap circuitry onboard a soundcard.
Micro line of product is probably a good start, though there are many others. At any rate you would have to go pretty far equipment-wise if you wanted to squeeze every droplet of juice out of HD650.
As for RCA input/output, you can just buy adapter cables from any audio accessory store. They then just plug straight into each other.