Depending on the hardness of the wood the drill size is a matter of choice. 75% engagement bit is 5/16 and tap is 3/8 by 16 for most stoppers.
Harder wood can come up in size a 64th or two to about 50% engagement.
Softer woods, I flood the threads with CA and after it sets, refresh the threads with the tap.
(There are a few 1/4 by 20 stopper bases, but do not remember them being stainless).