Computers are electrically messy, but that only matters if you're trying to get analog output. You're doing digital output, which the DAC in your receiver should reclock, no problem. Given your budget, an optical cable from computer to receiver is the way to go.
Alternatively, you could just play your CDs in your DVD player. You'd be using the same DAC, so the sound should be comparable.
Alternatively, you could just play your CDs in your DVD player. You'd be using the same DAC, so the sound should be comparable.