Another newbie question: What is a "small base
die" and when would you choose one of these over a standard die?

They further reduce the dims of the case. They are sometimes needed for reloading ammo for auto's and pumps. And perhaps lever guns. Rifles that do not have a strong camming action on closing.

Actually they size the case closer to the shell holder (pressure ring area), they don't push the shoulder back any further or make the shoulder/body any smaller than a standard FL die does.
IF your using a lot of brass that was origionaly fired in a MG or other oversized chambered gun, and trying to use it in a gun with a tighter chamber AND weak bolt camming than you may need one.