What you're asking for is a common scenario in feature selection. Stepwise methods are simple to run (only a few R commands), but it's also a greedy method. I don't think it's appropriate for me to repeat advantages/disadvantages for stepwise regression, please read:
Please note the R-square, F-statistic etc in the link all assume linear model is appropriate for your data, otherwise whatever you get might not make sense. Stepewise methods are generally don't perform very well practically, but it's certinaly better than random guessing.
Many statisticians prefer Lasso regression. You have a
shinrkage parameter that you can use to control the lasso effects. The first link has the details.