Just buy a NUC. I just bought a nuc, 2nd hand off eBay, the CPU supposedly has a 5W TDP... Adding a disk (WD Green?) it's probably going to stay below 10W
Intel NUC DE3815TYKE, Atom E3815, for about 50€ shipped.
It's got a DDR3 ram slot and can host 8GB ram, along with a sata port and a slot for a 2.5" disk. It also has 4GB of on-board storage that I really don't care about.
The processor is a single-core atom that clocks at about 1.4GHz with a TDP of about 5W.
I don't really care much about speed for this machine because it will become a home vpn gateway running PFSense. The CPU has AES-NI instruction, and that's what convinced me to get it.
My current vpn gateway is a Dell Optiplex FX160 which is still an atom and performs okay-ish, but has got no AES-NI and no internal storage beyond a dumb 2GB disk-on-module, on which pfsense barely fits and consumes about ~17 Watts powered on.
I've tested plenty at work and don't really have any complaints with any of them, worst case they will perform as well as an equivalent laptop and usually better due to more thermal headroom.
If you're optimizing for price and power consumption get an older SKU with an Atom, if you want more horsepower anything 10th gen with 4 cores will handle just about anything you can throw at it, and the idle power consumption is quite good too.
