Basically you want hardware that is a reasonable dual core x86 CPU at minimum. Since Intel chips doesn't really deprecate in price all that quickly, you're either looking at a G3258 (deprecated, but fits the bill), or some skylake chip. This excludes ULV CPUs, SoCs, anything AMD etc. if you look at haswell, I have a system with a G3258 that runs everything Dolphin can play at full speed at 4.2 ghz. If you get Skylake, you can get away with lower clock speeds, probably be fine for everything Dolphin.
And for the GPU, anything that is a notch above Intel HD graphics.
And for the GPU, anything that is a notch above Intel HD graphics.