I agree with Gus K, the jacks really don't matter.
The only thing I would consider if you get a 1/8" to RCA adaptor would be to try to match the metal to the metal in your sound card. If you have gold contacts in your soundcard's output jack, then get a gold plated adaptor. Dissimilar metals form corrosion over time, although it shouldn't make much of a difference, if at all.
Also, try to get the shortest cable that will reach from your PC to the target device, and keep the cable away from AC power cords.
The quality of the output of the soundcard and the source material plays a big role as well.
Something else to consider: You may have a "ground loop" where your PC is not at the same ground "level" as your target device (due to resistance in wires and poor AC connections mostly). Then you would get a hum. You could isloate the grounds but this takes special cables where there is a signal wire and then there are two ground connections: the shielding and another wire (like the signal wire). The connectors are hooked to certain wires at one end and a certain way at the other end (and it DOES make a difference which direction the are hooked up BTW). But this level of detail is really overkill and not necessary for your hookup unless you are excessively anal.
Taurus: Sharing a ground does not degrade sound at all, unless the outputs of your sound card happen to be balanced (which I VERY highly doubt). If they were balanced, you'd have to have 4 connections instead of 3, and the target device would have to have to accept a balanced signal (isolated grounds). There would have to be a different connection mechanism too; headphone jacks only have 3 connections.