I agree with Benjamin Crowell that, if you have the means, your first adventures into physics should be magical. This may be difficult to accomplish with commercial textbook.
I would strongly recommend
Matter and Motion by James Clerk Maxwell. Maxwell, as you might know, is one of the greatest theoretical physicists in the history of science. His writing is eloquent and simple. The book is very philosophical and motivated and thus provides a truly amazing foundation for not just physics but for all of natural sciences. Best of all, there is little mathematics involved. However, there is a lot of heavy thinking.
His writing, despite being written hundreds of years ago, reads like poetry. Here is a quote from the book explaining what we now call the homogeneity of space:
There are no landmarks in space; one portion of
space is exactly like every other portion, so that we
cannot tell where we are. We are, as it were, on an
unruffled sea, without stars, compass, soundings, wind,
or tide, and we cannot tell in what direction we are
going. We have no log which we can cast out to take
a dead reckoning by; we may compute our rate of
motion with respect to the neighbouring bodies, but
we do not know how these bodies may be moving in
space.
Beautiful! Do you think Giancoli discusses this, at least with such eloquence? Of course not!
Matter and Motion is the only introductory physics book I recommend for students lacking in calculus. Although it is without copyright and, therefore, legally available online,
Dover prints copies of it for cheap.
After
Matter and Motion, I would suggest you wait a bit before you pick up your second book of introductory physics. This is because calculus and geometry, which you may have not studied enough of, is the true language of physics.
NOTE: In most modern printings, the last chapter, "On the Equations of Motion of Connected Systems," was not originally part of
Matter and Motion, but was taken from
Electricity and Magnetism also by Maxwell. Unfortunately, It contains some Calculus as it deals with Lagrangian and Hamiltonian mechanics. However, since it was not originally included