While you can run an llm on an "old" laptop with an Nvidia GC it will likely be really slow. Like several minutes to much much longer slow. Huggingface.co is a good place to start and has a ton of different LLMs to choose from that range from small enough to run on your hardware to ones that won't.
As you are a teacher you know that research is going to be vital to your understanding and implementing this project. There is a plethora of information out there. There will not be a single person's answer that will work perfectly for your wants and your hardware.
When you have figured out your plan and then run into issues that's a good point to ask questions with more information about your situation.
I say this cause I just went through this. Not to be an ass.