Like others already advised you should be okay using an old laptop running Linux. Also get the paper server for minecraft as it is way more optimized than the vanilla servers

Edit: I almost forgot, using GraalVM instead of OpenJDK or whatever default Java installation is worth looking into. Doing that gave my Minecraft client a ~20% performance uplift

Also if you need help getting more FPS for a better (clientside) gaming experience feel free to reach out

Get a piece of junk old laptop or desktop off family, friends, the street, the ewaste pile at work or a local shop. Laptops with broken screens are perfect for this. Even old macs are fine, good use of them since its so expensive to replace their displays.

basically any 64 bit computer made in like the last 8 years will run paper well enough for a few people, i have a raspberry pi 4 with 4gb of ram doing exactly that and it works fine up until about 4-5 people are online at once.

Been there,

I started with a discarded desktop for my server, if you have choices you should probably focus on the fastest cpu clock speed. Cores don’t matter for Minecraft, any non broken minimum gpu will do as it doesn’t need to run the gameclient itself, Memory is the most easy part to obtain more of later. For just a mc server 4GB should do fine.

It be better to put a linux distro on it, currently my server is in a docker on Ubuntu. If something happens and it needs to restart the pc and docker can boot without even needing a monitor to login. It knows what to do and is very stable and reliable.

Of course if your like me at the start linux will still scare you. Go ahead and install the latest windows from the creation media thing from Microsoft. Provided you don’t care about personalization on the desktop you don’t need to pay to legally use windows. It wont be as reliable at times but otherwise work fine.

Big warning though, At some point you might end up with a custom build home theater server pc running with headless linux. not just minecraft but also numerous other self hosted things like cloud storage, media player,… I have a setup where i can insert old dvd into the server and it automatically rips and stores it on the server and i can just watch it on any pc or phone. Great if you have kids and a pile of old dvd in a local language that is hard to find online.

I cant tell you exactly how i got there since the days of running minecraft on a windows server, it just kinda happend organically.

Buy a used laptop or a a desktop (nothing fancy, office desktops can do the job) and run in on that.

If you can get your hands on one raspberry pis from the 3 onward will run Minecraft server okay. They don't consume much power but they're also much less powerful than a used desktop.

i can also recomment a barebone-pc like Gigabytes Brix-Series. You just add RAM (as much as possible) and a ssd, and you have a low power very capable Minecraft server (just like me) for about 250 bucks

Modded or vanilla? Bedrock or java?

Used laptop. Good CPU, ram, low power. Just make sure it's a 64bit processor.

It requires some technical insights but I've got a free server running through Oracle.

At first it's a Java server but with plugins also Bedrock players can login and play.

Since it's a free tier server, the resources are limited. But perfect for small households where the kids simply want a world to play on without the need of one of the devices being online.

Buy cheap mini PC and upgrade the RAM. I did that for Project Zomboid and it works wonder so far. I even have Tailscale installed so we can play anywhere

Java Vanilla: A Raspberry pi 3 or better would do the trick and not suck much power.

Alternatively there are servers that host a vanilla Minecraft instance just fine starting from like $4.50 to $6 for 3 months (a 1GB node)

Java Modded: Take an old laptop that has at least as much RAM you need to run the mods. A desktop is fine too but will draw more power and be costlier to run.

Install Linux, Java or OpenJDK, Forge/Paper/[Your Modengine here], Minecraft and the mods and you're all set.

If you're willing to get your hands a little dirty with scripting, once you know the command to start the server you can create a script that will re-issue that command if your server crashes randomly.