Just a note, the shields are expensive because there are people who have put quite a bit of time into designing the PCB boards for them, having them made, testing, etc. It is very possible to just purchase the IC's used on pretty much any shield and 'make' a setup yourself. For example, here's a site that goes through getting ethernet setup with an AVR chip - tuxgraphics.org: An AVR microcontroller based Ethernet device
Just note that when you begin making things like this yourself, it does occasionally get harder to diagnose problems because it could be a wiring issue, a design issue, or something similar
Proxying shouldn't be a huge problem if you understand the protocols involved.
If you are thinking about HTTP, you would then just have to specify the proxy server in your connect IP address, and send the proper headers to it with your web request.
Socks proxying may be a bit more tricky (because it is its own protocol) but even then, it isn't impossible - You just need to follow that protocol and connect to the socks server, then request a connection from it.
Now, all of this has a big caveat: If the proxy requires authentication, you would have to implement that protocol too. Hopefully it can use Basic (where you just Base64 encode your username and password) but if it has some more advanced authentication - you have to implement that.
Depending on what you want to do with the arduino ethernet connection, the proxy may or may not come into the equation. Using it as a server with the arduino outside the university - no problem, using it as a server inside, accessing it inside, it won't use a proxy usually but it depends on how your network manager has proxy exceptions set. As a server on the inside and accessing it outside, isn't a proxy problem its a firewall routing thing under control of the network manager. Using it as a client on the inside acessing outside , then then you have to negotiate the proxy, client inside accessing inside, again no proxy but it may have internal firewall issues depending on how its set up. Client outside accessing inside, again its a firewall routing thing.
In my other life I manage a school network............
Be careful at the cheap end of the market, its well worth buying one with the Wiznet 5100 chipset - much easier to program and easier on the arduinos limited resources. I bought one (a Wiznet) recently in the UK for £22 off Ebay including delivery. Translates to around $36 at todays exchange rates. The alternative ENC28J60 could be had for around £15