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Have you considered Fusion E350
? It's very energy efficient and reasonably inexpensive
If that lacks enough processing oomph for you, an affordable Socket-AM3 solution with integrated graphics should suffice, though it will use a bit more power.
Here are some micro-ATX socket-AM3 motherboards with the 880G+SB850 chipset and USB3:$95
Stick a cheap Athlon II X2 255
or Athlon II X3 450
processor on there, add 2x2 or 2x4 GiB of PC3-12800
or PC3-10600 memory, and you should be well on your way.
Sandy Bridge on LGA1155 would be more energy efficient, but it costs a lot more, too. Matching the Core i3-2100T
with the P8H67-M PRO/CSM
or a combination of Core i3-2100 + H67 motherboard
would be good examples.
You could also do well with an older Clarkdale processor on LGA1156. Pair up the Core i3-550
with the GA-H55M-USB3
, for example, but it's not really any cheaper than the superior Sandy Bridge options.