I feel like in fan fiction, Logan is normally cast as the PE teacher. I hesitate to give him that role for some reason. I think people might underestimate how PE teaches things like stretching, how that changes, Logan’s willingness to test to be certified for teaching and/or attend conferences to follow education standards as new research comes out.
But hear me out - I think he is better suited as the groundskeeper. Especially in the movieverse setting post X2 where Logan is at the start seemingly freeloading off of the school while it operates. He starts of with subtle things that just annoys him - like a creaking sound on a cabinet. Just put some WD40 on that. Then he notices a worn panel, probably damaged by a student with overactive powers. No worries - Logan found some tools in an outdoor shed and builds a new panel and installs it.
The other faculty and students don’t notice it but then start to realize slowly that… the drawers open more smoothly. The wood finishes seem more shiny and new. That fence has a fresh coat of paint. The kitchen sink stopped dripping. Eventually, the students catch on and they ask for Logan to fix things in their room. It starts off with a student who is embarrassed to tell the teachers that he burned a piece of furniture when accidentally using their powers. Then Rogue complains about a wobbly chair in her table within earshot of Logan and he comes over and fixes it. Jean mentions that she needs to replace a piece of exercise equipment in the gym and Logan offers to pick it up and install it. Instead of taking the car into a mechanic, Scott consults Logan first about an issue with one of the cars and they’re able to figure out what’s wrong on their own instead.
Charles eventually brings up in a faculty meeting how nice it is that they haven’t had to hire contractors lately to fix things around the school. It’s normally a pain to vet contractors to make sure that they aren’t anti-mutant or make arrangements to keep the mutant school thing a secret. But now Logan seems to have naturally taken that role in the school. Logan has no comment on the matter and is regularly absent during staff meetings.
He can still be a substitute teacher (in a pinch), proctor tests, lead X-team trainings, supervise the kids during field trips, lead extracurricular activities like outdoor trips and martial arts. I believe in the DoFP universe where Logan is a history teacher in the Howard Zinn style of "bottom up" vs "top down". But I just feel like groundskeeper is more realistic imo.
Side note: Maybe I just overvalue my PE education because as a 30 year old I am so appreciative of learning how to stretch. I don’t think Logan would bother or know like the most recent changes to exercise best practice for an updated curriculum. I also went to school in California when Arnold Schwarzenegger was governor and he implemented a lot of state educational policy where students had to be tested on several things like mile times, bmi, endurance, strength, etc. As an unathletic nerd, I remember it because it source of stress if I couldn’t pass these assessments. And again I think that administrative burden doesn’t feel like something that Logan would bother. I do think it’d bother the faculty if it’s not done because they do want the students to matriculate to colleges should the students want to pursue higher education. That requires meeting accreditations standards regardless if the school has secrets about the paramilitary training and the mutant social services.