For what it's worth, I'm doing roughly the same thing, though starting with linear algebra. At first I started with multivariable calc, but when I found it too confusing, people advised me to skip to linear algebra first and then return to MVC, and so far I've found that that's absolutely the right way to go. I'm not sure why they're usually taught the other way around; LA definitely seems more like a prereq of MVC.
I tried to read Spivak's Calc once and didn't really like it much; I'm not sure why everyone loves it. Maybe it gets better as you go along, idk.
I've been doing LA via Gilbert Strang's lectures on the MIT Open CourseWare, and so far I'm finding them thoroughly fascinating and charming. I've also been reading his book and just started Hoffman & Kunze's Linear Algebra, which supposedly has a bit more theory (which I really can't go without).
Just some notes from a fellow traveler. ;-)
I tried to read Spivak's Calc once and didn't really like it much; I'm not sure why everyone loves it. Maybe it gets better as you go along, idk.
"Not liking" is not very specific. It's good all else equal to "like" a book, but all else is often not equal, so alternatives should be compared from other points of view as well. It's very good for training in rigorous proofs at introductory undergraduate level, if you do the exercises. It's not necessarily enjoyable.
...I've also been reading his book and just started Hoffman & Kunze's
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.