One thing to keep in mind is that unless you’re planning on actually installing said games on these machines you’re going to have some trouble playing them off of your hard drive. When an application or game is installed entries referencing the location where the software is on the HDD are made in the operating system’s registry—you can think of it as a sort of index for the operating system that contains information it needs to run any installed applications.
There certainly are exceptions to this rule but you’ll probably have a heck of a time in some cases.
One more thing to take into consideration is the computers in the lab and what they’re capable of. I noticed everyone here is mentioning newer and as of yet unavailable interfaces in the case of USB 3.0. If the computers you’re using don’t have eSATA or Firewire 800 then there’s no point in buying one of these more expensive options. A USB 2.0 drive is most likely you’re best option—3.0 should work on a 2.0 system but it won’t be taking advantage of the increased transfer speed available.
Remember, playing games off of an external drive is tricky. There are ways around it in some instances—I’m not particularly sure if they can be talked about here—but the best thing to do is when you get your HDD, test it at home, make sure the games aren’t installed on your machine but are only on your HDD. That being said, do a bit of reading about external drives. Like Waffle said if the machines in the lab have eSATA or Firewire 800 get something capable of that as those are fast but if not and if you’re willing to wait for USB 3.0 that would be ideal. Though in the end I can’t imagine you’d be disappointed with a USB 2.0 drive.