Also most newer cards, even the fairly older ones mind you, don't nessiccarily need to be 1:1 scale (square). They can be rectangular in size as long as both dimensions are each power of 2. So for example a 'modern day' card should support 512x1024 sized textures, but it never hurts to test this.

There is a tool that used to be hosted on Delphi3D.com before when the site was still online. It was a great resource from way back that has since turned into a ghost site and eventually inactive. It was called glinfo and when ran, it would tell you exactly what maximum size your textures could be on that system. Great for testing systems and your development system to set yourself a target minimum/maximum for OpenGL version and specs.

There is this other one now that should work for most platforms that you can develop for using Object Pascal. It's called GLview 3.0 and it'll work on win32/64 and Mac OS X as well as iOS and Android devices too. Maybe see if they'll let you run this program on your school? It was approved for the iPhone/iPad by Apple so that kinda says something. Worked alright when I ran in on my devices.