What are the "basics" of college?

If you can, I think you should talk to an advisor at the college you've been admitted to and see what they can help you plan out. I'd also get in touch with their financial aid office and see if there's anything you can get from them. There's a limit to how much people here will be able to help you without knowing more about your situation, but there might be ways to make college affordable for you and your family without going the community college route.

Usually people go to community college for two years and then apply to transfer to a four-year school to finish their degree; when you apply to the four-year school first, they're usually not expecting you to take the first two years at a CC. You would probably need to apply again (there or somewhere else) in two years and be accepted as a transfer student after you've finished your courses at the community college level.

However it can also be a bit more complicated than that. The best strategy if you want to do two years at a CC and two at a four-year college is to find what's called either a "guaranteed transfer" program or an "articulation agreement." Some CCs will have a deal with a specific four-year college where that college guarantees to accept that student and their transfer credits as long as they complete their CC courses. If a school doesn't have that kind of agreement, it's not guaranteed that a four-year college will actually accept all of your community college credits, and you could end up still going there for three or even four years to finish everything.

As for the "basics" that you're asking about, "General Studies" will mean fulfilling the basic requirements in math, literature, science, and social studies that most colleges will make you take in your first two years (it's honestly a lot like an extension of high school). It's not really the same thing as a major; instead, it's what you would take at a four-year college before starting your major. The letters you're seeing are all different types of Associate's Degrees (Associates of Arts, Associates of Sciences, etc.) that you get from a CC after finishing those general courses. So the one you select would depend on what you eventually want to study.