Mitch, there are lots of choices, but this is what I do.
I first drill a hole in the bottom center of the blank about 1/8" deep with a 7/8" forstner bit. Then I drill a hole for the stopper with a 9/32" drill bit. Then I use this PSI tapping tool to cut threads in the blank:
Bottle Stopper Drill and Tap Set at Penn State Industries
Then I use this stopper mandrel from Woodcraft:
Buy Whiteside Adjustable Stopper Mandrel at Woodcraft.com
I use this drill chuck from Woodcraft to hold the mandrel:
Buy Heavy Duty 1/2" Keyed Lathe Drill Chuck #2 MT at Woodcraft.com
The forstner countersink provides a smooth transition between metal & wood and hides any imperfection if the bottom of your blank is not perfectly perpendicular to the threaded hole.
The PSI tap set comes with a 5/16" drill bit, but I prefer to use a slightly smaller 9/32" bit. I don't have any trouble tapping hard woods with a 9/32" hole, but I have had some tear out issues when I tried to tap a 5/16" hole in soft woods (like unstabilized spalted woods) - I have not had any issues since switching to the 9/32" bit.
I like the Woodcraft chuck because it has a threaded end so you can screw a drawbar into it through the head stock which will keep the MT2 taper of the chuck from coming out while turning stoppers & such.
I use a mandrel saver for pen turning, so when I start turning a stopper, I bring the mandrel saver up to just barely tuching the end of the blank to help keep it stable while I turn it round. Once I get the blank rounded, I back the tailstock out of the way & finish turning.
Another hint - once I get the stopper turned to shape, I unscrew it from the mandrel then screw it back on to just barely touching the mandrel surface before I start finishing it. If you don't do that, it can sometimes be a bear to unscrew after you have completed the finishing. DAMHIKT!
I use the standard & mini 3/8" x 16 stainless steel stoppers from Woodchux, but there are a number of other highly regarded sources of stoppers.
Bottle Stopper Kits - WoodChux Woodturning
Hope this helps. This is just one way of making stoppers - it works for me but YMMV.
Edgar