"What issues might I run into and how do I avoid them?"
On the older devices, especially ISRs, setting a location (usually local flash) for the IOS .bin image, and setting it up to boot, is often all it takes to run that IOS. Often, but not always, boot rom versions images don't matter, but release notes would describe dependencies. (Unfortunately, for EoL devices, that documentation might no longer be available.) Things like web management support, though, usually are best installed via an installation package. (I assume you might be able to manually set such [i.e. web management] up, not something I've ever done. [I have, very often, just copied .bin images about, as I didn't bother with web management, and it was a tad "faster" than using an installer packet - though also easier to make a mistake, too.])
"How easy is it to revert to a prior image?"
Again, excluding things like web management, often the same procedures as moving up to a new .bin, just the reverse for reverting. One thing to watch for, when you upgrade an IOS, unless it's a huge version jump, if there are any syntax changes, the newer version will almost always auto convert the config file to the new syntax. Going backwards, an older IOS will NOT recognize newer syntax. So, it's a good ideal to have a saved copy of config file that matches the IOS it originally used.
Now the above, just addresses your questions, technically.
Legally, you cannot move to a "better" feature set, nor a newer IOS, without having a support contract and/or paying the additional licensing fees. I suspect, your university would not want to bump into the penalties for such violations.
However, I believe (???), you can downgrade IOS version or feature set, to less than what the Cisco device had been originally licensed for, or up to less was whatever IOS version that was current at the end of a support contract. This might be an option, to have the same set of devices running the same IOS and with the same feature set.
BTW, are you aware of Cisco's Packet Tracer?
