Hardware

If you already know your hardware you can probably skip this step.

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You can use whatever hardware you want, but it can't be too old or slow. It all depends on what you're trying to do. Small or big population, vanilla or modded?

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Vanilla (PaperMC) - easy to run, can get away with less RAM

Modded (Forge) - much harder to run, needs strong CPU and RAM

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For Minecraft, focus on single core performance. There definitely are benefits to fast multi-core processors, but a lot of the game sits on 1 thread. World generation and chunk loading (with PaperMC) will definitely benefit from multiple cores. I would look towards a strong quad core or better, like an i5.

 

A solid state drive (SSD) is pretty much a must-have. They're cheap these days and the performance benefits are huge. Minecraft does a ton of reading and writing to the disk so slower media will hurt. If you're planning on running a larger server, consider an M.2 NVMe drive. Even if the motherboard doesn't have M.2 you can use a PCIe card - it doesn't need to be your boot drive.

Repurpose an old PC you have laying around, or pick one up cheap off eBay/Facebook marketplace/OfferUp/etc. You can find Dell/HP “workstation” desktop PCs with a ~4th gen i5 or i7 for under $100. 

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Here's an example from eBay. Should be good for most small-medium servers.
Solid state drive, 8GB of RAM, i5