After asking this beginner's question, I took people's advice and started test driving bicycles. I rode for about twenty minutes, so not too long. About fifteen minutes later, I found that my right thumb had developed a serious uncontrollable tremor. Whether I clenched the thumb or relaxed the thumb, it kept shaking. The left was not shaking.
I test drove two bikes (both relatively upright): one where the hand grips + brake handles fit well (though I didn't have padded gloves so that caused some pain) and the second where the brake handles were far enough from the hand grips that I could only reach them with my finger tips. I returned quickly with that bike because it hurt and I didn't feel safe being unable to control the brakes well.
I had ulnar nerve problems with that hand/wrist twenty-odd years ago, though the ulnar nerve numbness ran from my pinkie and ring fingers up to my neck and didn't involve my thumb at all.
Is the thumb tremor simply a result of bad-configuration-for-me handles? Or is it a symptom that I haven't ridden in forever? Was it the lack of proper padded gloves? All three?