You can mine with a Ras Pi if you want.
I mine with a small 10" dell notebook - 1.6Gh possessor / 2 GB ram, with Windows 7 Starter operating system running off a USB stick (memory sticks consume less power than HHDs that have a motor in them), ....
However; it is the "Bifury twin chip USB mining sticks or ASIC devices that are pluged into the notebook that do all the hard work and not the notebook itself.
Buy yourself a "GekkoScience USB Compac BTC Miner (8-16 GH/s @ 0.3w/GH)"
its a good place to start for under $60. You can plug it via USB into anything Pentium 4 / Windows XP (2 GB RAM and an interet conection) upwards and you will soon be mining small fractions of a bitcoin.
Hope this helps