You need this: http://mitpress.mit.edu/SICM augmented by e.g. Lanczos Variational Principle (the closest to a platonic ideal of exposition for this didactically elusive topic) and various lecture notes for classical mechanics courses http://www.damtp.cam.ac.uk/user/tong/teaching.html. From there move to Byron & Fuller Mathematical Physics and only then you may question where to next, that's the bare minimum of theory in physics. Baez & Muniain "Gauge Fields & bla bla" has very good narrative on one offer what to do after, Sethna Statistical Mechanics on another. Speaking of bare minimums there's a youtube lecture series by Susskind "Theoretical Minimum of Physics" or sth.