Okay so you want to host a minecraft server with (I'm assuming) your own hardware to prevent monthly fees. Well this can technically be done with just a spare computer that's laying around... really improves the experience if you can get a computer with type higher performance processor. If you can find a spare used desktop that has say maybe a quad core (i5 maybe?) and 8gb ram should hold up okay.

Now the software you run is going to be a rather loaded question in this sub. There are many different versions of the Minecraft server software. Each version providing its own benefits and losses. For the sake of simplicity I'm going to recommend spigot. Just install the latest version of Java download spigot and you're off to the races.

Now let's move on to the networking... If you plan to have this computer sit at your own house setting this up will be rather simple assuming you have decent internet. Just log into your routers settings page and do some port forwarding.

If you want to have this set up at your school and leave it at the school... That really depends on how well your school's IT department is willing to work with you. If it's a good IT department they'll be excited to help you (mostly because this is going to be the most interesting thing they'll do all week).