It might vary depend on where you were taught and resources available. My instructor had all sorts of types of firearms out and we had hands-on time with all of them; but we only talked about the storage requirements

Sure but it's still only a few weekends long of a course, and there should be actual practical at the range

This is so confusing because; handguns are just as loud, rodent control is best dealt with an air powered gun, and unless you're going out to specifically do that task you wouldn't be bringing your tool.

You mean like putting an animal out of its misery? Well the proper way to do that would be to call a vet, but if you wanted to shoot it, a rifle would not necessarily be too bulky