From what I understand, there are 3 main types of predictor selection method for linear models, namely, 1 Subset Selection, 2 Shrinkage and 3 Dimension Reduction.
The subset selection includes the Best Subset Selection and the Stepwise Selection which could be forward, backward or hybrid. AIC, BIC, Cp or Adjusted R-Square can be used to select the predictors.
The Shrinkage includes the Ridge Regression and Lasso. This approach attempts to shrink the coefficients to 0
Dimension reduction transforms the predictors and fit the model using the transformed predictor.
If forecasting accuracy is my main goal and model interpretability is not important, which method(s) should I use ? What should I do if the methods give inconsistent results ? What are the main advantages and disadvantages of each approach ?