I am sure you have probably heard buy a cheaper carpet and better pad. There may be some truth to that statement, however, In general, the rule of thumb for most residential carpet applications is to choose cushion no more than 7/16 inch thick do to the fact that the tack strip which the carpet is stretched upon is 7/16" high thus making a flat surface.
When considering the density of pad realize that most carpet manufacturers prefer 8 lb pad and that support will help your carpet perform the best without bottoming out!
When trying to decide which pad is right for your application after the understanding of what height and density of carpet then the chose is about how you like the feel of the carpet padding and which pairs best for your lifestyle.
Areas like Steps and family rooms with extra traffic might consider a denser pad like felt or rubber pads.
Area rugs and berber or a low profile carpet, choose a cushion no more than 3/8 inch thick with 8 pounds density for the best performance and support.
When putting new carpet it is always the Best solution to replace the padding, do to the fact if your pad bottoms out before carpet is ready to be replaced you will have to live with an uncomfortable walk and potentially ridges through out carpet..