My first recommendation is to take classes based on your interests and intended college major(s). Other than that, core subjects are more important than elective subjects. Here is a very approximate classification scheme.
Core Academic AP Classes
Biology, Calculus (AB & BC), Chemistry, English Literature & Composition, Physics 1, Physics 2, Physics B, Physics C: Mechanics, Physics C: Electricity & Magnetism, U.S. History, U.S. Government & Politics
Elective Academic AP Classes
Art History, Comparative Government & Politics, Computer Science A, Computer Science AB, Computer Science Principles, English Language & Composition, Environmental Science, European History, Human Geography, Macroeconomics, Microeconomics, Psychology, Statistics, World History
Foreign Language
Chinese Language and Culture, French Language, French Literature, German Language, Italian Language and Culture, Japanese Language and Culture, Latin, Latin Literature, Russian Language and Culture, Spanish Language, Spanish Literature
Other
Music Theory, Research, Seminar, Studio Art (2-D, 3-D, & Drawing)
There’s no reason to self-study unless you want college credit for a class your school doesn’t offer or that doesn’t fit in your schedule. If your school offers a given AP class, colleges want you take the class and the test rather than just the test. If your school doesn’t offer it, colleges don’t expect you to take it, and you’d be better off working on your ECs or studying for the SAT or something.
Colleges judge you based on what your school offers. My school only had four AP classes when I went there, so it would have been unfair to expect more than that.
It’s important to keep in mind that advanced classes are beneficial for lots of reasons other than college admissions. My advice is to take the hardest classes possible while keeping your unweighted GPA above 3.5. Obviously, it can be lower if you go to a difficult high school where you’d be the valedictorian with a 3.5.
You need to challenge yourself if you want to be prepared for college, but some universities have hard GPA or class-rank cutoffs for scholarships, honors programs, etc.
Most of them have prerequisites.
AP is better if an AP equivalent for a course is available at your school, especially if the dual-enrollment class is taught in your high school building, because AP exams are standardized and college classes aren’t. Otherwise, dual enrollment is fine, though it can be logistically difficult if you have to run back and forth all the time.
In most cases it’s also easier to get credit for an AP test score than it is for a dual-enrollment class, but it’s not like you can never get credit for dual-enrollment classes. Some colleges have weird rules about how you can’t get credit for a dual-enrollment class if you used it to meet a high school graduation requirement, or if it shows up on your high school transcript. Check with the colleges you want to apply to.
[url=http://talk.collegeconfidential.com/discussion/comment/17052213#Comment_17052213]Here[/url] is a longer post I wrote about the benefits and drawbacks of dual enrollment.