Ah, right - fair enough.
Therefore I'd suggest you just use the HDMI port on the monitor (which is probably what you already do).
As for blu-ray movies - what do you mean play them at 120Hz? The source movies should only be 24Hz, so won't really look much better on a standard 120Hz monitor. If you want them to to look smoother in motion then I would suggest getting a TV which uses the interpolating technology to add extra frames (by guessing - effectively) - often they are advertised as "600Hz" or similar. This makes the video looks smoother, but there can be some issues when changing scenes.