Reddit mentions of Introduction To Commutative Algebra (Addison-Wesley Series in Mathematics)

It's "MacDonald", not "McDonald": Introduction To Commutative Algebra

Let me back up a step to make an observation: I get the sense you're... impatient, maybe? That you've heard about all this really really cool stuff in math, and you want to get to as much of it as possible, and right away, too.

So, for example, you're trying to get through Hubbard... and Spivak's Calculus on Manifolds... and maybe Rudin's PMA... or in the alternative, Abbott—but all simultaneously. What you seem to be finding is that by trying to eat everything in one bite, you're choking.

Now, you don't have to limit yourself to doing everything in sequence: first rigorous one-variable calculus, then linear algebra, then higher dimensional calculus, then metric spaces and general topology. But right now, it probably feels like you're trying to write a novel in a foreign language before fully understanding the vocabulary or rules of grammar or whatever.

So, for example, keep in mind that Spivak's Calculus on Manifolds assumes as a prerequisite something equivalent to Spivak's own Calculus. If you haven't already established that background first, then you'll have an steep uphill climb to follow what's going on in Calculus on Manifolds.

Now you'd be correct that there's all this really cool math just over the horizon. The catch is that there's really no shortcut to getting through the prerequisites before you can even understand let alone appreciate the more "advanced" stuff.

As for your Topology book? I think it would be a pretty beginner-friendly introduction to topology, which would be appropriate for you. I don't think you'd need it in the context of, say, learning Abbott. Topology is important, of course, but you wouldn't need to learn it in order to understand Abbot or Spivak's Calculus. (You wouldn't necessarily even need the full generality of point-set topology to understand Rudin's treatment of metric space topology.) The Dover series has the advantage of being affordable, which can be really important in a field where even short, paperback textbooks of less than fewer than 150 pages can be over $70. One tradeoff is that Dover textbooks are typically relatively old. That doesn't always matter, but older textbooks are more likely to use out-of-date terminology or notation or both. It probably wouldn't matter here for this book, but it's worth keeping in mind going forward.

I'd focus on linear algebra separate from one-variable calculus. If you have enough time, you might be able to study both simultaneously. If not, I'd do one, then the other. A dedicated book or books on linear algebra might be better than the abbreviated version of linear algebra you'd find in PMA or Calculus on Manifolds or something else. Without knowing more about your background—both in terms of linear algebra specifically and your fluency in proofs more generally—I wouldn't know what textbook to recommend. But since books can be expensive, I'd recommend trying to find options at a nearby college or university library. (From context, I'm assuming you're either an undergraduate student, in which case this should be straightforward, or you're an ambitious high school student, in which case you may have geographic and/or transportation constraints to consider.) If you can really luck out, a teacher or professor would be in a good position to evaluate where you are now, as well as what would be an appropriate roadmap for where to go next.

I hope this has been helpful and relevant to your questions. Good luck!

Nobody's mentioned Atiyah and MacDonald yet. I am very surprised. Not only is it well-written, it has a superb collection of exercises that will bring you further along in knowledge as you do them.

Introduction to Commutative Algebra by Atiyah and MacDonald. Not suitable for your first algebra textbook, but an awesome subsequent text.