I'm running a study to test whether personality (Big Five) predicts problem-solving in children ($N=200$), and was wondering whether anyone could help with the best approach for analysis. I've collected personality data for the Big Five on a 5-point Likert scale with 4-6 questions per facet (openness, extraversion, agreeableness, etc.). I want to see whether personality ratings predict how children solve problems. I have two types of data for the problem solving. One is binary (whether they solved it using method $X$ or $Y$), and the other is continuous (no. of different types of specific behaviours used when solving the problem).
What would the best way to go about the analysis? Would I take means of each of the five types of personality and categorise participants as high/low. So, for example, participants below the group mean of extroversion are introverts and those above are extroverts, and then run analyses after that? Or perhaps run t-tests for the binary data: Test for differences in mean scores of each of the personality facets across those who use method $X$ and method $Y$?
Or is there a way to correlate the data? Perhaps correlate scores of personality facets with frequencies of the specific behaviours?