How to choose best model for Regression?
I think a better option will be that you try different regression techniques (it will be good for your learning curve) and see advantages and disadvantage.

For subset selection purposes few options are:

1- Best subset selection : in which you start with a null model and fill all possible combination of models and select best model on the basis of AIC, BIC or adjusted R2.

2-Forward selection: You start with a null model as well and add feature one by one to see which one gives lowest RSS or highest R2. Then add another feature again until you have the best model.

3-Backward selection: you start with a model with all p predictors remove one predictor evaluate adjusted R2 or AIC, BIC. do it again and again until you have a satisfactory model.

You don't have to do it manually both R and python have library that will help you in this.