Angela -- the three taps are set to cut threads in solid material. The taper tap has a long tapered section and starts easily. With a "blind hole" - one that is not drilled all the way through, it will not cut threads to the bottom of the hole or even close. A plug tap has less taper, but is harder to start threads. It leaves the last few threads uncut. The bottom tap is hard to start because it has no taper to line up the tap in the hole. It does cut all the way to the last bottom thread. Many like to start with a taper tap because the tapered section lines the tap up and get the threads started. A plug tap cuts more threads riding in the threads that the taper tap started. The Bottom tap finishs the threads all the way to the bottom. If you drill the hole just a little deeper than the threads on the bottle stopper, and you are patient, you can use a plug tap to do it all.
Normally in wood, a 5/16 hole is the correct size for a 3/8 by 16 threaded hole. A 21/64 or 11/32 hole may work better for threading polyester resin. I have one blank, but have not drilled and tapped it yet.
Do get a tap wrench to put threads into bottle blanks. It is better balanced for getting threads started. You do not need a big one for 3/8 or smaller threads (Note that the Berea bottle stoppers = the ones with the small diameter taper at the bottom -- use a smaller connecting rod - 1/4-20 if I remember correctly).
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