I've taught out of the first three of these. If I had to pick one for a first study, I'd vote for Strang -- and watch his videos while you go. Our second-semester mostly-math-majors linear algebra course uses Axler, which I think is nice for the purpose, but our students already have done a semester of computational stuff first. (Though the complete absence of any computations in the book means they don't always connect the material from the two courses very well.)