[server] Create an apt-mirror only containing absolutely essential updates and packages?

I'm doing some volunteer work for a rural education institution. They do a lot of installs and reinstalls of ubuntu that require updates and a few select packages from the repos. The inteet out here is terrible, and they have very limited resources. Setting up a VM apt-mirror would help a lot, but from what I see it requires a 100GB+ download - that might not be a big deal to a lot of you working in professional environments, but for this school it's enormous.

Is it possible to set up a VM with apt-mirror or a similar app that only pulls the essential security updates and the select few packages/dependencies they need for class? If so, how would I go about it?