Using a Raspberry Pi is massive overkill. A $20 XBee module, a $3 microcontroller, and a custom PCB will do the trick; you can then control it all from your PC with another XBee radio. It'll probably be easier than making Linux deal with your relay, because microcontrollers are easy mode. Even an Arduino would be expensive overkill for this project.
Once you add a power supply for your micro, connectors, and an enclosure, you'll probably be hitting the $50 mark, if not more.
You also need to be very, very careful when working with the mains. I wouldn't route a board that works with it unless you know exactly what you're doing.
It'll probably be easier than making Linux deal with your relay
At least on the Beagleboard, GPIOs show up as files that you can write 'high' and 'low' to, making it easy to switch relays.
How is it is massive overkill? The total amount of structure is the same in both of the solutions. Only in the one you mention it has less gates. Same amount of input resources. Gates a free. 5 years from now kids will be making LEDs blink using vixie cron and a python script talking the GPIO lines of a 32 microprocessor and this is O.K.
I think you mean the ATMega168 and its power consumption is somewhat less than 0.0027W, while the BCM2835 is more like 2.5W, but regardless, I think you're defining overkill in terms of power, which is only one dimension, probably not the one the comment was referring to.
It's a bit like saying using a tungsten lamp is massive overkill in lighting a room.
