Connecting through your proxy server is no harder than it might be at home - you simply set your default gateway for any machines you'll configure for school to point at the proxy server. Will act in exactly the same way as a broadband route at home might.
If you're wanting to give it a go, work out what people at school, students + teachers, would want out of a system such as web, e-mail, office suite, photo editing, etc. Haven't looked at Edbunutu, but know a few schools with some small installs just of Ubuntu and find it works well, especially with KDE tweaked to look fairly similar to Windows. I'm not a fan of that at home (Fluxbox all the way), but in a school, you'd need something that didn't look to foreign. Stick to Firefox, Thundebird + OpenOffice and you should be fine. Msot teachers don't like change so are likely to turn their noses up unless it's familiar enough to sit down and work with.
Even with a small machine acting as a server running NFS for shared network drives, maybe Samba to connect in to a couple of Windows shares to demonstrate you can integrate with your current Windows servers, and half a dozen workstations would be cool to setup and shouldn't be that hard. If you're dealing with older machines, hardware configuration might be a problem, but will at least tax your brain a little!
Plus, there's plenty of people on here to lend a hand with any of the network configuration you might need