There is no ideal text for a beginning one semester course as taught
in the US to first or second year college students.  Older books like H&K 
treat only the abstract theory, in a fairly conceptual way and (if I recall
correctly) with maps written on the right contrary to what students do in
calculus.    A later generation of books like the original Anton are also
pure math books but start by overemphasizing unrealistic manipulations with
small matrices and vectors; then there is an abrupt shift to abstraction.
Determinants are presented in a purely computational mode, as though they
were really used for this purpose; then eigenvalues occur very late and again
in oversimplified small examples.   Fortunately the newer texts tend to mix
pure and applied throughout, but as a result they contain far too much material
for a first course.   And eigenvalue theory still gets introduced very late.
Strang is attractive in many ways, but too loosely written down and not 
suitable for an inexperienced reader without a reliable guide at hand.    Aside
from Strang, the emphasis in most US textbooks remains placed on unrealistic
integer calculations with very small matrices rather than on the geometry of
subspaces, etc.   The pervasive role of geometric thinking in the subject is
mostly downplayed in texts, as is the role of analysis.  For self-study,
something like Friedberg-Insel-Spence may be the best compromise choice.