I have taught GRE classes for a national company for a couple of years. I also took the GRE twice, raising my score from the 75th percentile to 99th percentile. So I am very familiar with the test, and I can say unequivocally that you should not take a prep class (even the ones that I teach).
Don't get me wrong: I am completely confident that my courses--and other courses out there--benefit students. The problem is that students could raise their score just as much by studying on their own. These classes aren't mustachian.
I could probably talk about the GRE for way too long, but I'll just list off a few thoughts:
1. Most courses/books are written for an average test-taker. That means the focus is on helping a student in the 40th percentile get into the 60th percentile. If that's you, then any of the books out there should be great. But if you are shooting for a very high score, you will quickly grow out of the books put out by the two largest test companies. I recommend Barron's if you are shooting for a higher-end score. Do every problem in the book.
2. The practice tests put out by ETS (the testmaker) are a valuable resource. They will be your most accurate benchmarks along the way. Because of this, you should plan to take these at strategic points (i.e., don't take them all at the beginning). I recommend taking the first ETS test after a week or two of studying.
3. There is a HUGE learning curve on the GRE (especially the Quantitative). Studying makes a world of a difference. But that said, most books don't offer enough practice. You may need to purchase multiple books.
4. The math on the GRE really only goes up to a 10th grade level, but the GRE still has VERY tricky problems. Fortunately, there is only a finite number of ways that ETS can make tricky problems using 10th grade math. That means your goal should be to see EVERY trick that ETS can throw at you before test day. You should know how to solve EVERY quantitative problem in Barron's (or some other book) before your test. Even if you are good at math, you need to do a lot of practice in order to learn how the "moves" that the testmakers use to make 10th grade math very difficult.
Just to illustrate this: many of my students (especially math/econ/physics majors) are much better than I am at math. I'm embarrassed to admit that I have never even taken calculus. But I can absolutely crush the GRE quantitative -- I scored an 800/800 on the old scale. And when I teach, I have a couple dozen problems up my sleeve that trip up almost all of my math/econ/physics students. That's because GRE math is a beast of its own. But once you figure out the 50-or-so ways to make 10th grade math difficult, you know how to solve every GRE math problem. And that's a beautiful thing! Long story short: even if you are good at math, getting extra practice on the Quantitative will really pay off.
5. Vocabulary is incredibly important on the Verbal, but the amount of time you study vocabulary depends on how much total time you have on your hands (so if you begin studying only a few weeks before your test date, I wouldn't spend much time at all with vocab). Start with any of the focused lists (300-500 words) that the major test companies publish. Any of these lists will work.
6. However, the GRE Vocabulary is the one part of the test that you will continue to use throughout your graduate school career. So if you have a longer period of time to study, you have multiple reasons to improve your vocabulary. Barron's has a 3500(ish) word list that I worked through before my test. It took about 6 months, but I'm grateful that I improved my vocabulary.
7. Don't have any ego battles on the Reading Comprehension. We all think we know how to read, so this is an easy section to neglect (or not trust the book when it tells you your answers are wrong). Whatever resource you are working with, pay attention to WHY certain answers are incorrect.