In a dataset of two non-overlapping populations (patients & healthy, total $n=60$) I would like to find (out of $300$ independent variables) significant predictors for a continuous dependent variable. Correlation between predictors is present. I am interested in finding out if any of the predictors is related to the dependent variable "in reality" (rather than predicting the dependent variable as exactly as possible). As I got overwhelmed with the numerous possible approaches, I would like to ask for which approach is most recommended.
From my understanding stepwise inclusion or exclusion of predictors, is not recommended
E.g. run a linear regression separately for every predictor and correct p-values for multiple comparison using FDR (probably very conservative?)
Principle-component regression: difficult to interpret as I won't be able to tell about the predictive power of individual predictors but only of the components.
any other suggestions?