I'm relatively new to statistics, and I'm searching for an answer as to which regression method would be most appropriate for the problem I'm facing. My task is to use a number of continuous predictor variables (up to potentially 20) to predict a continous outcome variable. However, I don't know which variables are significant, which will be useful or not, and hence I assume I must go through some kind of step by step process to find the best variables to use. Is there a method that would be most appropriate for this? Perhaps relatively easy to use software that accomodates this method?

Also when entering these variables into software, is it necessary to test the relationships between individual predictor variables (should they be added, subtracted, multiplied, higher order operators etc?)

Thanks in advance,

Marty