I’ve been using a Gigabye Brix i7 system to host Avalon (Twinktown) for a few months now and it seems to work OK. It is similar to the Intel NUC. What I like about it is small, has SSD and uses only 60 watts max… or at least that is what it says. I got it originally to host my Open Sim regions (which I still host from it along with HiFi) and regular web server because where I was living at the time had very poor internet connection so I just set it up at a place that had good internet and controlled it remotely.
When I first got it I opted for Win 7 rather than Linux mainly because I wasn’t sure what I would be using it for.
If I were you, I might not think so much about the minimum but more about the best performance and long term usefulness verses cost and also how much content you want to host from it. I thought about using one of my old unused machines or to build up a new system for it, but decided it might be better to use a tiny system like the one I bought.
If I were doing it now, and only running HiFi on it… I might just opt for cloud server. But maybe not… just because I like having more control over everything. Hosting assets and ACs on it are a different issue. I don’t have enough experience with either… so you should probably ask others because I really don’t know what I am doing.
edited to add: I guess it all depends on what you think your time is worth… for me: time is expensive, RAM and CPU are cheap, etc.