I believe my course used Halliday, Resnick, and Walker, but at the intro level, basically anything should do.

I wasn't even really thinking about the integration with programming - the parts I've used have mostly been just knowing what the basic equations were, along with representations like vectors and such. If you have a function of t, then all you need to do to simulate it is advance t by some infinitesimal amount (based on the frame rate, usually) and then compute your new positions. I guess that when you get to more complex simulations, then things like fast matrix multiplication and symbolic differentiation may be useful, but I've never actually used them in my own programming.