[I'm a physics professor, for what it's worth, and I've spent more time than I care to admit trying to find a good textbook for this.]

For folks with a programming background, I suspect it would be hard to do better than Matter and Interactions by Chabay and Sherwood. (Someone already mentioned this elsewhere in the comments here.) It makes substantial use of Python code in the text and problems, and (partly enabled by that) it takes a delightfully modern approach that discusses the true (relativistic) formula for momentum (etc.) very early on. I haven't taught out of it yet, but I've been very tempted.

I'm currently teaching the intro course using Tom Moore's Six Ideas that Shaped Physics series. His approach is a little quirky at times, but usually for good reasons. I like it a lot.

Those are both purely introductory texts (though both cover topics up through "modern" physics: relativity and basic quantum phenomena). Beyond that, well, that's a bigger question.

My favorite go-to book for basic physics is the 1966 edition of Haliday & Resnick, which you can still find on Amazon as a combined two volume book, I think. The newer editions are quite watered down, but they do an acceptable job. There's also a newer, more advanced version of these books called Physics, Volume 1 & 2 by the same authors that you may consider checking out.

Books are hard reading though, so video lectures are also the next best option. Walter Lewin does a good job with this, so try googling his lectures.

Also, you'll probably want to stay away from Feynman lectures until you actually understand the theory.

Leonard Susskind's Classical Mechanics course: http://theoreticalminimum.com/courses/classical-mechanics/20...

Julius Wess: Theoretische Mechanik

The book is amazing, since it introduces advanced concepts like group theory and greens functions very early with very simple examples from classical mechanics. Unfortunately it is only available in german, yet:

http://www.springer.com/de/book/9783540885740

Feynman lectures -> Landau Lifshitz, when you can make the jump.

This will show you how to do the physics, then (Landau Lifshitz) show you how to reformulate this physics (again, it is actually in the feynman lectures too) in the terms we use in modern physics (Variational methods etc.)

Feynman lectures are excellent for physical intuition but if someone doesn't have a few years of practice with physics it will be difficult to get much out of it. Feynman also doesn't have a lot in the way of problem solving, even with the companion problem solving book.

With that in mind, Landau/Lifshitz is an entirely different class. I'm a practicing astrophysical theorist and I would never claim to have grokked these volumes in anything nearing completeness. A serious post-PhD program of study can be undertaken to understand to the finer points of those books; this is a pursuit that would challenge any practitioner. (I place Physics of Shock Waves and High Temperature Hydrodynamic Phenomena by Zel'dovich and Razier in the same category of extremely information dense Soviet tracts on physics.) They are incredibly valuable, although I do think there is a bit of an element of "if you don't know L/L, you aren't a real theorist."

I think that recommending these texts is great for someone down the road, but if someone hasn't even had a full year of intro physics recommending these is not appropriate. Intro-level textbooks exist for a reason - not all of them are cheap, watered down versions of the "real stuff." (Some are, of course.) There are also some texts I've found (but don't remember, unfortunately) in the computer vision community that introduce some physics that would be great for someone with a computer science/engineering background.

edit: "cheap" as in "cheap feeling" not inexpensive, as most of those intro texts are more expensive than the graduate level

The first L&L book is what I'm thinking of: It's actually pretty manageable. I'm talking out of my ass beyond here in the series, I don't have any others in physical form so I've read bits of QM and The classical theory of fields

The downside to them is that they don't come into contact with the "mathematical" physics side e.g. Treatment of Lagrangian/Hamiltonian formalism through differential geometry.

If you want a good textbook, try David Morin's "Introduction to Classical Mechanics: With Problems and Solutions". Rather rigorous book with a good writing style and a lot of exercises.

You can take a look at Feynman lecture notes at caltech.edu.

Mentioned in another branch of this discussion, but I really liked "From Newton to Mandelbrot" for a computational take on learning Physics.

John Taylor "Classical Mechanics"