It doesn’t take much, really. Invoice Ninja itself could probably run on a toaster. It’s the database that determines just how much you need to throw at it. For a home or small to medium business, still not much.
The main thing you want to look at is storage. The more things you have (or plan to have) in your database (especially if you attach files to your invoices), the more space you’ll need. But if you’re going with a mini PC setup, it will be more then enough. People have gotten it all running on a Raspberry Pi, so any “normal” PC will work just fine.
Basically, if it can run a LAMP stack, it can run Invoice Ninja. My personal setup is an Ubuntu 18.04 VM. Two cores, and 2gb of RAM. Right now it’s using just shy of 400mb of that RAM for everything. Drive usage is at around 6.5gb, but I do a lot of other things with that VM, so your mileage may vary.
Bottom line, if you’re buying or building a new system for Invoice Ninja, unless you need to store a LOT of attachments in your database, you’ll be just fine with whatever you get.