Minimal set of new predictor variable(s) and added value to existing predictor

Hi everyone,

I am working on gene expression data for 15 genes and am supposed to derive a minimal predictive set of genes that can be used as a marker profile for disease progression.
So far, I created Kaplan-Meier curves for all 15 candidates and performed tested for association with bad outcome using random assignment of labels and bootstrapping. Two of my genes were significantly associated with disease progression, while two others were on the border of significance.
My search for a method to solve the remaining two tasks led me to stepwise regression, however, after reading that this method is not considered ideal I would like to know what other options I have to obtain a minimal predictive set of genes.

In addition, I was asked to check the added value of all of my genes when comparing them to established clinical markers, but unfortunately I did not find a method to do so yet (which might be due to me using the wrong search terms...).

Any help is greatly appreciated.