
On the outputs, use XLR to the monitors, or balanced (i.e. DIs with two RCA inputs like the ART DTI are a good fit, you can then use a cheap 1/8" to cinch cable to connect your computer.

You'll need a stereo model to convert each of the two mono channels to balanced. The second-best possibility is to make a balanced signal from your unbalanced output: this is done with a BalUn, or, as it's more commonly called, DI Box. Professional audio interfaces have such outputs, so the best solution would be to get one of those. However, this only works right when you also have balanced outputs. Professional mixers or active speakers have balanced inputs instead, which work fine even if the lines are hundreds of meters long (live) or you need very low noise (in the studio). Unbalanced stereo, as used by consumer-device headphone- or line-outputs, is virtually never used in the professional sector, because it often has trouble with interference (ground loops, dimmer buzz etc.).

As Todd Wilcox said, this is a phasing issue you're only hearing the stereo difference.
