The first 1x1 round bricks had no lip, just like most bricks:
A lip was then added:
Later, a hole was added in the stud:
Was that to prevent choking, as in some minifig heads?
The full-base 1x1 round bricks were produced from 1955 until 1963, during the period when LEGO pieces were made from cellulose acetate (CA) plastic, but were sold until about 1966. According to Gary Istok's Unofficial LEGO Sets/Parts Collector's Guide the solid-stud full-base 1x1 round brick was only ever made from CA plastic. After the supply of them ran out, a new design was adopted with the "tapered" bottom and made from ABS plastic. (Chapter 51, p. 3)
The reason for the change may have had something to do with the fact that the old full-bottom bricks did not grip very well. Also, the tapered-bottom bricks not only fit over a regular stud but fit in between top studs, making them more versatile than the older style.
The hole in the stud appeared about 1977 and was in response to product-safety regulations. Other cylindrical pieces like minifig heads were also given stud holes. This was because it was thought cylindrical pieces were more likely to completely plug a nostril or throat. The solid-stud minifig head has made a comeback recently, however, as these regulations have changed.