Ok let's go from the bottom up, I will list what I have in my library, that I also think will guide you very nicely:
Any decent Pre-Calc book should review all of t basic high school math (algebra, geometry, trig) plus some sort of introduction to limits. With that in mind, here are preliminary books:
"Precalculus: Functions and Graphs" by Swokowski and Cole 9th Ed can serve that purpose, through in all honesty I've never used my book all that much.
"Conceptual Physics" by Hewitt 8th Edition - Very easy to read text on physics, that really doesn't require much math at all, but never the less treats the subject in more depth than "popular science" books. 8th Edition should be VERY VERY VERY cheap by now.
Beginning Books:
"Calculus For Dummies" and "Calculus Workbook for Dummies" by Ryan will offer you a very informal intro to Calc, and get you into the groove of how to DO calc problems.
"College Physics" by Serway. 7th Edition. Algebra/Trig based physics text that is very clear, yet has nice challenging problems that are sometimes at the level of a Calc based physics text. Again, 7th edition should be available for dirt cheap.
First Year Science/Math/Engineering Major level texts:
"Calculus" by Larson, 4th Edition. My favorite calc text. I've had the 4th Edition since 1995, and to this day I still find myself cracking it open for clarification on some topics. Again, any edition that is not the absolute latest will be found for next to nothing!
"Physics for Scientists and Engineers, with Modern Physics" by Serway, 6th Edition. Like my Calc book, this book is very clear and I often find myself referring to it again and again! And again, 6th Edition can be found for cheap.
At this point, you may want to being to supplement your reading with less 'traditional' texts that still treat the subject somewhat seriously. You might want to begin reading The Feynman Lectures on Physics at this point. Start at Volume I and go from there
Second Year Texts:
The Larson Calc book should suffice for Calc III type of stuff. As an alternative, you can try:
"Second Year Calculus: From Celestial Mechanics to Special Relativity" by Bressoud. The plus is that you get Calc III from the point of view of physics, essential Calc III taught for the sake of preparing you for Physics specifically. The minus is that it might not be the easiest intro to Calc III. Also, don't really think this can be found very cheaply.
"Elementary Linear Algebra" by Anton, 7th Edition. Some people don't like Anton because its "too easy." But I don't see the problem with this. At this point, you need a working knowledge of L.A., you don't need a rigorous one (yet). Since you are self-studying, you will do better with getting your feet wet on a "simpler" text like this. Again, 7th Edition should cost nothing
"Introduction to Ordinary Differential Equations" by Ross 4th Edition
"An Introduction to Ordinary Differential Equations" by Coddington
"Ordinary Differential Equations" by Tenenbaum
Are all great. You don't need three of them, just one will suffice. The last two are Dover books, so they are cheap. "An Intro" is more basic, quick and dirty than "Ordinary" but "Ordinary" contains much much more material.
If you've bought a version of Serway's "Physics" text that includes Modern Physics, then you are fine there. If you don't have a version of Physics that has a Modern Physics section, or you want a more in depth intro, try:
"Modern Physics for Scientists and Engineers" by Taylor 2nd Edition. Not sure if you can find this edition for cheap, but "International" versions should be found for "OK" money.
Now, supplemental texts to the above can include:
"Understanding Quantum Physics: A User's Manual" by Morrison. Not cheap, but very well worth the money
"The Mathematics of Relativity for the Rest of Us" by Jaggerman. Not expensive, but not cheap either, again, very much worth the money.
"Div, Grad, Curl and all that" by Schey. Very clear, concise intro to vector calc (a topic of Calc III), with the goal of solving basic Electrostatics problems. 2nd Edition can be found for cheap.
"Quantum Mechanics in Simple Matrix Form" by Jordan. Very easy to read book, gives you a slightly different way of looking at QM (through matrices). Its a Dover book, so its very cheap.
Must Have References for higher level physics:
"Mathematical Methods for the Physical Sciences" by Boas. Essentially contains all the math above (and much more), but in a reference type of style (not suitable for learning the material for the first time, but very helpful if you've already seen some of the material). Usually not cheap.
Now you can look at some junior/senior level physics texts:
"Classical Mechanics" - Taylor. Probably can't be found cheaply, but also the most "wordy" and probably the easiest to understand of the standard Theoretical Mechanics books.
"Introduction to Electrodynamics" - by Griffiths. Not cheap if not an "International Edition". Also not an easy book, problems can be really difficult, but I am not really aware of an alternative. The book is well written to be sure, and its interesting to read, but at this point, things begin to get thick real fast.
"Introduction to Quantum Mechanics" - by Griffiths. I tend to feel that E&M is much harder than QM at this level. But this book is written in much the same style as his E&M book, so you will come across some very difficult problems. Still, a very well written book, and for the level it is written at, its hard to think of an alternative (usually alternatives are grad level books).
"Gravity: An Introduction to Einstein's Relativity" by Hartle. The natural next step from the Jaggerman text. Can be difficult, but again for an undergrad level course, its hard to come up with an alternative that treats the subject at this level.
That covers the core of nice library of books for the self learner (and a uni student as well). If you are also interested in math at the level a Math major would tackle, let me know.
