If you know one of your computer is always up, you also have the possibility to use it as an ssh proxy.
let's say your have a domain name setup for your external IP address (i.e myhome.dyndns.com or whatever), what you will do is connect on one computer (let's say raspberry is always up, and you forward the port from your router to it), the your ssh connections will be:
school --> (router, transparent here) --> raspberry --> ubuntu or windows
now, in your ~/.ssh/config at school, add the lines:
Host ubuntu 192.168.1.51
Hostname ubuntu (change to match your setup)
User myraspberryuser (change it ;-) )
IdentityFile ~/.ssh/id_rsa (The path to your private key, on the school computer, better on an usb key if public computer)
ProxyCommand ssh -W %h:%p %firstname.lastname@example.org
To connect then:
ssh-add ~/.ssh/id_rsa # to do only once per session
ssh myuser@ubuntu (login without password)
From now, if you type ssh ubuntu, the computer will first connect to the raspberry, and then start an ssh session to the ubuntu computer.
I recommend you, whatever the port you choose to forward, to disable password in /etc/sshd.conf to permit only login through ssh key. This way, if you setup the key on the raspberry and on ubuntu, with the parameter 'ForwardAgent', you will have to only unlock the key and then no password is required to connect. This way, even if bots are trying to login on your ssh, they will never be able to login since you disallow password logon.
Bonus, this works also with scp, scp foo ubuntu:/tmp/foo will use the same setup without further parameters.
Bonus 2, this setup does not require any change at home, if tomorrow you and another computer, just copy/paste the code in your ssh config, change the host and ip, that's it, no need to open a new port on the router