I agree Axler would be very tough the first time through, but that would also rule out Hoffman-Kunze.
For a basic introduction, there is a book by Gareth Williams that goes into applications and is at an understandable level.
For me, I like to use two different books. I read through a basic...
You could try Axler's Linear Algebra, which makes little use of determinants. I have heard good things about W.H. Greub's book. Finally, as already mentioned, there are many free books on the Internet. In particular, there is a very good set of notes by a Stanford Professor at...