Basaltic ones from lava flows on larger asteroids or Moon or Mars. Another meteor crashing into another planet, moon, or asteroid would kick up material, a very tiny percentage of which would find its way to Earth. Edmund Halley noticed that the comet of 1682 was in fact the same one seen on other occasions. Because he was right, it's named after him. Comets get named after their discovers, usually amateur astronomers observing in their backyards.
Most comets are only a few kilometers across.
Made of water, methane ice, ammonia ice, carbon dioxide ice, and dust. It exists whether the comet is close to the sun or not. The nucleus is a few kilometers across. Dark, lumpy potato-like thing. The coma is the dusty and gassy atmosphere around the comet as it gets close to the Sun, and the surface material starts sublimating.