If you are looking for 'best' predictions (i.e., regression-based estimates, not necessarily forecasts), then I think graphics are often helpful, such as Figures 5 and 6 in the following, but you may 'overfit' if you do not save out some test data:
There is no perfect model in nature. To ascertain the effect of a variable over another there are many possibilities. Regression and correlation are the twin possibilities especially in a directly bivariate scenario. If repeated measurements are made and if more than one independent variables are involved ANOVA could be applied. Model comparison can be done by diagnostic checking to know the better or best model.
You can use regression analysis, if your data is continuous. The model form has to be defined by you. You may seek the help of literature or go for hit and trial method or you can use your acumen to adjudge the model form.
Most of the statistical software has the facility of Regression analysis, however model form has to be defined by the researcher himself.