Sharing Mac mini with monitor in another room. (also bluetooth keyboard/mouse with second monitor)
A couple of options for you...

You could use an Apple TV connected to your monitor and connect to your Mini using AirPlay - since 10.9 you're no longer restricted to using AirPlay to just mirror your main display, you can use an AirPlay-connected display as a secondary display.

Otherwise you're looking at a hard-wired display setup. Hard-wiring may be cheaper, it all depends on the length of cable-runs as you may need to look at active video signal boosters/extenders for longer runs. If your existing Ethernet cabling is point-to-point and you've a cable that runs from your main room to your secondary, you could use DVI-Ethernet extenders. These use the cabling to transmit video directly rather than actually being connected to the home network.