Primordial rocks are those that initially formed in outer space as the solar nebula collapsed to form the Sun (and ultimately the planets). These objects coalesced to become comets, asteroids, meteoroids, and ultimately the planets. Their characteristics vary according to where they formed, how large they became (which affects subsequent processing of the primordial material), and their history of collisions and proximity to the Sun.
The solar nebula began as clouds of cold gas and dust collapsed under the weight of gravitational self-attraction to form a spinning disk with a thick, dense core. The core contracted quickly until fusion ignited in its center, forming the Sun, and the dust and ices clumped together into millimeter-scale bodies called chondrules arrayed into a nearly flat disk spinning around the Sun.
Then things started to get interesting. The heat of the new Sun vaporized volatile materials, providing a strong gradient of composition. Only the most refractory of minerals could survive near the Sun, while ices such as methane, ammonia, and water could only condense near the orbit now occupied by Jupiter or beyond. Gasses vaporized near the Sun, however, were blown out by the radiation pressure of light (and the early solar wind), only to condense again as they moved far enough away from the Sun. Meanwhile, friction in the disk caused a gradual spiral of material toward the Sun. Radiation pressure and the solar wind would have pushed smaller particles away from the Sun while having little affect on larger ones, although near the plane of the disk the volume of dust would tend to shadow the matter further out. All the while gravity tended to draw these particles together into larger bodies we call planetoids. These planetoids (typically one to several kilometers wide) would not be affected by solar radiation, but would collide into larger bodies called planetesimals (several to dozens of kilometers wide), which in turn would collide into planetary embryos (hundreds of kilometers wide), which in turn collided leaving the current planets in the solar system. The bottom line was that the early solar nebula was a churning caldron stirred by the heat and light of the Sun, pushing volatile materials outward while gravity and friction pulled material toward the sun.
While the bulk of many asteroids is composed of chondrules, there are light-colored inclusions (especially common in carbonaceous chondrites) called CAIs, or Calcium-Aluminum-rich Inclusions. These may also pre-date the formation of our solar system by a few million years.
There are many meteoric minerals found in meteorites (and thus asteroids) which are extremely rare on Earth, including moissanite (SiC), Schreibersite (a rare iron nickel phosphide mineral, (Fe,Ni)3P, common in iron-nickel meteorites), and xifengite (Fe5Si3).
Some of the rare minerals are found as presolar grains, likely formed well before our Solar System.
Tiny diamonds (C) have been found in meteorites, but the most common gemstone found by far is peridot (olivine); some stony-iron meteors may be sliced and polished resulting in a beautiful stained-glass-window appearance of transparent green peridot crystals in an iron matrix.
See The Evolution of Minerals which describes the changes found in mineral species over time.