Gilbert Strang's "Intro to Linear Algebra"[1] is widely recommended and I enjoyed it as a supplement to Friedberg, Insel, and Spence's much more formal "Linear Algebra"[2].
I learned right from FIS without any "warmup" from Strang-level material and it was rough to say the least. I came away with a good final grade and a very poor understanding of most of what I was doing, I was just grinding through proofs with little practical intuition. Good reference book, but very difficult to learn from, especially with a professor who seemed to love abstract math and didn't place high value on geometric intuition.
In general, proof-oriented undergrad classes for Linear Algebra would be either the second class they take, or it's a math major going a pathway specifically for math people. Similar to Sheldon Axler's famous book.