Since you specifically asked about hardware, I have found that, to date, the best small form factor pc to use for dedicated emulation is this guy:
Pair it with a high-clock desktop Kabby Lake CPU, like this:
or, better yet, this:
add 2x SO-DIMMs (for symmetrical dual-channel):
-and you have a really powerful emulation setup!
Only, the problem is, the GPU might be an issue for what you want to do. You could definitely get by with the CPU’s iGPU at base resolution (maybe even 2x), but if you want to make everything as pretty as possible by cranking up the render resolution, anti-aliasing, anisotropic filtering, etc., etc., that integrated GPU won’t be able to handle it. Where does that leave you? You could get a dedicated card, but as @anothername99 has correctly pointed out above, Nvidia is out of the picture… AMD is too, really. Whether it be missing features or lack of performance, both Nvidia & AMD have lacking driver support for Linux. You can read the many different articles on the web covering this issue.
It’s unfortunate to say, but if you’re looking at specifically emulating GameCube\Wii your best bet, really, is to do so under Windows with an Nvidia or AMD card, as the drivers are optimized for that ecosystem… With Laka (Linux) you would be getting reduced performance because those vendors refuse to spend money and time to create quality drivers for Linux. For example:
And, as much as I love Lakka and LibRetro, the official version of Dolphin for Windows would also be a better choice since the LibRetro port is still a work-in-progress as it doesn’t perform as well and lacks some features. One day though we will have our cake and eat it too damnit!
Good luck, and post back with an update as to what route you went