When I was in school, I took great pleasure in the lectures by Prof. Walter Lewin, physics professor at MIT, but now retired. His style of lecturing is quite unique and got him rather famous on the internet. All of his undergraduate lectures have been video-taped and are available through MIT's OpenCourseWare program.
As for the mathematical prerequisites, Calculus is sort of required. I'm afraid there's not so much you can do without it. But you may just ignore the bits you don't understand yet and review them later. Anyways, classical mechanics is a very useful thing to have in mind when learning about Calculus. It's what Newton developed calculus for!
When you mastered classical mechanics, you can just proceed with electrodynamics which is a little tougher on your mathematics. But, again you can just give it a try and -- having the physical application in mind -- you might find multi-variable calculus way more intuitive when learning it with the neccessary mathematical rigor.
Regarding quantum mechanics, I wouldn't touch that. Often, when people are discussing quantum mechanics without the proper mathematical tools, they end up talking about things like "wave-particle duality" or (even worse) Schrödinger's cat. This will leave you more confused than before and give you the impression that there's some spooky magic to QM. It's not. It just requires lots of math.