Single Board Computer Recommendations

[Levi Pearson]

Using a Linux-powered SBC to control a few relays seems like
mega-overkill.  Sounds more like a job for a microcontroller.  Getting
ethernet and/or wireless hooked up to a microcontroller is less
trivial than hooking one up to a Linux SBC, though.

The big problem is that although the chips are individually extremely
cheap in quantity, by the time you get to the point of low-run
single-board computers, it's hard to get what you want for under $100.
 You can only get cheap electronics due to economies of scale;
electronic devices are really expensive to engineer (from a consumer's
price point of view, anyway).

You could easily pay way more for a development board with cheap specs
than you would for a Beagleboard, which as you say has an incredible
amount of processing and I/O on it (but no ethernet!).  It might even
make sense from a cost perspective to use a Beagleboard and a
USB-to-Ethernet dongle.  Or even repurposing an old laptop with a
broken screen, if size is not an issue and you can find one for cheap.