You are not dumb. You need a little more information and more experience.
You are lucky, a goliath I is a good sounding 410. It is really the cabinet that started the massive shift to 410 ported bass cabinets some time around 1980 or so. That design still works fine, but has been surpassed, IMHO.
Distortion comes from a lot of places, but the only kind that harms speakers is that caused by asking them to do what they cannot do. Sending a signal that asks them to move farther than they are designed to move will eventually burn them out or tear them up.
Heat build-up and mechanical over-excursion are both caused simply by playing (generally low frequencies) too loud.
Distortion from your pre-amp (gain), your amp (master volume), an effects pedal, etc. will NOT by themselves harm your speakers.
The problem is that all those other sources of distortion or extreme signal complexity will make it impossible to tell if your speakers are distorting.
Speakers complain before they fail. They make ugly sounds that mask the actual pitch. The intended waveform of your instrument is not correctly reproduced, and frequencies that don't belong to a given note obscure what should have been there. Sometimes it is a rattle, sometimes popping, sometimes clicking or even burps, fuzziness, or "farts."
My advice is as follows:
1) Get your goliath I fixed. It is a cool cabinet that is rare and worth keeping around in working condition.
2) Get a newer second cabinet that weighs less and can handle more power. Having the goliath as a back up or rehearsal cab would be good.
3) Experiment with your new amp head and cabinet. Get to know their limits.
4) Carefully supervise and use of your gear by others.
5) Wear hearing protection at all times in a loud music situation.