Hi Timothy,
Is it possible to build something like I describe which uses under 30 Watts, and if so, what hardware would people recommend?
I am very happy with several mini-itx systems, both from VIA and from Jetway.
For instance, a VIA VB7002 with 1.5Ghz C7-D CPU and 2Gb of RAM cost me 89 euro's, including 19% VAT. A kernel build takes some 15 minutes and a full `make build` 120 minutes. I'm using this baby for a low power server, so I'm not bothered by the Unichrome graphics thingy.
Intel has a few mini-itx desktop boards, both with Atom and Celeron CPUs that are dirt cheap; I have a few of those running perfectly aswell.
You could equip them with 2.5" harddisks to keep the power consumption pretty low, probably below 30 Watts.
Good luck!... Nico