A properly fitted velvet, linen or cloth kippah is often worn with no clip at all and stays in place well, especially if you have fairly short hair. On the other hand, knitted kippahs almost always need a clip to keep them from falling off. Satin and leather yarmulkes are somewhere in between. Some cloth and leather kippot now come with a built-in hair clip.
Knitted kippahs vary in quality. The best type are known as DMC. The term DMC is an abbreviation of Doffus-Mieg & Compagnie, a renowned yarn company in France which the the leading knitted kippah manufacturers rely on. In recent years linen and cloth kippahs have grown in popularity.
When shopping online, the easiest way to determine the right size is to find a kippah at home that fits and measure the diameter. When kippah sizes are listed, the number refers to the diameter of the kippah measured across the top (not the underside).
Is there a minimum size requirement? In his responsum in Igros Moshe (vol. 1, OC 1:8). Rabbi Moshe Feinstein states that a kippah should cover the majority of one's head, noting this is a stringency, rather than an absolute requirement. The minimum required size is for a kippah to be big enough to be considered a covering rather than a decoration. According to Rabbi Ovadia Hadayah, the kippah must be visible from all sides, otherwise it would not be considered a covering (Shut Yaskil Avdi, Vol. 6, p. 292). Similarly Rabbi Ovadiah Yosef held that “it should be recognizable and visible from all sides of the head, front and back” (Shut Yehaveh Da’at 4:1).
In practice, some Israelis (Religious Zionists) wear small, flat, knitted kippot (and sometimes leather), Conservative and Reform Jews in the US tend to wear larger kippot and Chareidim typically where large velvet kippot.
Some people wear a kippah all the time, while others keep their head covered only in synagogue and special occasions; then there are some people in between. They may keep a kippah handy in their pocket at all times, should the need arise, and they debate just putting the kippah on – and leaving it there, come what may. If you fit the latter description, the following links may be helpful: