For me, the answer depends on: (a) what your research question is; and (b) how many variables are involved. If just two variables are involved, and you want to know whether scores on the two variables are related, the regression R and simple, bivariate Pearson r will be exactly the same in magnitude (regression R is typically reported on 0-1 scale, whereas Pearson R is typically reported on -1..0..1 scale). In either approach, the Pearson r shows the amount of expected change in the dependent variable per unit (here, Standard Deviation is the unit) change in the independent variable. It will be the same numerically and in sign as the "standardized regression coefficient" (sometimes called 'beta') in bivariate regression.
If you have more than two variables, and your question has to do with how a set of (two or more) variables collectively relates to scores on a single dependent variable, then multiple regression is preferable to running (and only running) sets of Pearson correlations.
I would propose that you start by getting a scatter/dot plot to visualize the relationship between the numerical variables. Then you can follow the detailed advice according to @David Morse