I'm taking College Algebra this fall (Math 111 at my school.) Math has never been my strong point and it's something that I've always struggled with a lot. School starts on September 25th, and I want to use the time before then to brush up on my Algebra skills.
I don't have the syllabus yet, but here's the course description:
An introduction to functions from symbolic, numerical, and graphical points of view. Topics include polynomial; logarithmic, and exponential functions; inequalities, absolute value equations and inequalities, systems of equations, conic sections, and mathematical modeling. This is a challenging and technical course primarily intended for those majoring in Mathematics, Physical Science or Engineering. It is a preparatory class for the four-term Calculus series.
Course Outcomes: Solve polynomial, logarithmic and/or exponential equations, and interpret their solutions. Connect functions and conics to their visual, verbal, or symbolic representation. Provide a detailed analysis of the graph of a function. Demonstrate understanding of the notation and algebra of functions.
So, what is the best/most important thing to study?
I have taught College Algebra a number of times, and can recommend two pretty good books. The first is Dave Cohen's book, he who lectured at ucla for many years.
The second is by Gustafson and Frisk.
All the topics you listed would be important, btw.