My school's network only allows access to certain websites only if you're on the school's network. When I am home however, I cannot access these websites.

To solve this, I was thinking of setting up a linux box on the school's campus and rerouting my home traffic through the linux box. I'm not too sure on the terminology or how this would be accomplished.

So I was hoping for something like this:

My computer sends request to server. Server accesses the resource I wish. Sends it back to me.

So the Server acts as my window to the internet

MY COMPUTER --> SERVER --> INTERNET

And if I go to whatismyipaddress.com from my computer, it should show the ip of the server since all my internet traffic is being routed through there.

So, how would I go about doing this. Would this be setting up a proxy server? Are there any proxy server distrobutions? Or is it something else?

There is more than one way to do it.
One way is to tunnel the X port.

Use any distribution that have ssh, X and a web browser (almost all distributions, including livecds).

from your home,
# ssh remotehost -R 6000:localhost:6001
... enter the password
# export DISPLAY=localhost:1
# your_browser your_site

Or, if you are daring, set up a full-blown VPN.

Another way is to ssh tunnel the http port (80).