I'm planning to host around two or three Minecraft servers and want the strongest setup possible for roughly $200. I'm considering an older, inexpensive platform such as fourth-generation Intel with DDR3 to keep costs down. The servers would probably use only a few mods or plugins rather than huge modpacks. I also need advice on the CPU, RAM, storage, and whether a GPU is necessary. For the case, I currently have an Adidas shoebox available, although I realize it may not be a safe or practical enclosure.
2 Answers
For Minecraft servers, prioritize CPU single-thread performance and enough RAM over a graphics card. A used office PC with a fourth-generation Core i5 or i7, 16GB of DDR3, and an SSD would be a reasonable starting point. You can run a headless server without a dedicated GPU, though the system still needs some basic video output for setup. Look for a complete used desktop rather than buying every part separately, since $200 is tight. Also, don’t use a shoebox as the case—airflow, grounding, dust, and fire safety are real concerns. Use the original case or an inexpensive compatible enclosure instead.
The exact requirements depend heavily on player count and the type of mods. Three lightly used vanilla or lightly modified servers can run on an older six- or eight-thread Intel system, but large modpacks, lots of players, or terrain-generation mods can demand much newer hardware. I’d search for a used business desktop with a Core i7-4770 or similar, 16GB or 32GB of DDR3, and a SATA SSD. Spend the remaining money on reliable storage and cooling rather than a GPU. Use a lightweight Linux server installation if you’re comfortable with it, and make regular backups.
A few plugins or small mods are very different from heavy modpacks. Ask how many players will be online at once before choosing the hardware, because that matters more than simply counting the servers.

If the servers are lightly populated and only have a few plugins or mods, 16GB should be workable. Leave some memory for the operating system instead of assigning all of it to Minecraft.