Even quite recent and well performing hardware can give low power usage these days. For example an Intel i3 CPU on a power efficient motherboard, combined with a SSD and powered by a PicoPSU should be able to run idle under 20W.
But keeping the amount of CPU usage to a minimum is just as important though, or in other words: the software you use.
When I look at what my VM's consume
in terms of CPU, I see that there's 1 VM that's performing worse than the rest; that's where the Plugwise Source is running, using 10 times more CPU than the 2nd most-CPU-consuming-process on that particular VM. If you have too much of those CPU hungry applications/services running, it will be much harder to accomplish your goal, no matter what hardware you use. It's all in the mix