I want to plan the next few subjects I learn (by self-study) in mathematics. I have made it through the equivalent of maybe half a Calculus I class so far, but I would like to start a bit on linear algebra and/or differential equations (which I will not do until maybe I work on my calculus some more). Is it a good idea to take this path?
It's probably better to learn linear algebra independently of differential equations at first, and then see how vector spaces and eigenvalue problems appear in systems of ODEs. Of course, you want to make sure you get a decent book for self-study. Gilbert Strang's book on linear algebra is great if you want something that is focused on applications (but still contains some theory). A more theoretical approach would be Axler's "Linear Algebra Done Right."
I had begun Linear Algebra when I was doing Calculus, and didn't encounter any issues, but you will definitely need aspects of Linear Algebra and Calculus in differential equations, so I wouldn't start that yet.