Minecraft – How to set up a Minecraft server on a specific port

Technically, I think the query port is UDP while the game port is TCP, so they should be able to share the same port number.

this is because only traffic from certain ports can get outside the network

Are you quite sure? Because if that was how it worked, you would be unable to connect to the Internet. "Random port over 50000" sounds like you're talking about the ephemeral port range.

It is more likely that your school restricts the remote ports that you can access. Your network admin would have to allow outbound traffic to port 25565, or alternatively you could run your server on a port that is already allowed. Port 80's a pretty safe bet.

The local port Minecraft opens on your machine is randomly assigned by the operating system and should not factor into this at all. Pretty much any program that opens a network connection has to open up a random port to receive data.