Logistic or Random Forest? I have data on various standardized tests that certain students took and whether or not they ended up passing a specific class in college. Using the pass/fail as the dependent variable and the different scores on the test for the independent variables, I would like to figure out a metric that best predicts the students success in that class; i.e., Student gets these scores on these tests hence the probability that they pass is so and so. 

Logistic regression is my first instinct but I was wondering if there are other, possibly better, ways to approach this problem.
In general, it's never a bad idea to use logistic regression as a first stab at a classification problem. If it doesn't work great, it at least gives you a baseline. Random forest would probably work well here as well. Generally, random forests aren't considered very interpretable, but they're actually pretty interpretable if you're interested in understanding the decision process for a single prediction, which it sounds like would be sufficient for your needs here (i.e., the model can tell you a student is likely to perform a certain way because of their behavior on specific tests). A random forest will probably also handle missing data better, which might be useful to you since I'm guessing not all students took the same tests.

Another option you can try here which handles null data extremely well and would also be simple for inference, is naive bayes.