STEP ONE: Take the density of the planet, if a chunk or terrestrial, and look up the composition on 3.1.1. (For gas giants and asteroids, skip to THREE/4 and THREE/5. Small chaunks are best treated as single asteroids. (THREE/4).
BASIC PLANETARY STRUCTURE:
All planets aside from the smallest chunks and the gas giants have three layers, the core, the mantle and the crust. Lighter materials tend to end up in the crust and heavier, like metals, in the core, through the process of differentiation all larger chunks and planets go through. An inner zone planet with high density is thus likely to have it because it has a big metal core, not because all the material is composed by heavier elements. An inner zone planet with low density comparatively has a small metal core, or perhaps none at all. In the outer system metals are comparatively rare, so the core (heavy material) is likely to be silicates (rock) and the lighter crust and mantle more composed of ices, such as water, ammonia, carbon dioxide etc.
CORE: The core of a world is the densest part. It may be molten or partly molten. Some small planets and chunks in the outer system may have a not-very defined core very similar to the mantle. Comparatively large cores may indicate that parts of the mantle has been blown off by early impacts during system formation. Outer system cores are typically made of silicates to a high degree.
MANTLE: This part of the world lies outside the core but inside the crust. It can be molten, semi-molten or solid. In worlds in the inner zone, the mantle is generally a mix of silicates and metals, while in the outer system the mantle is commonly made of ices.
CRUST: The surface region. Density of the crust is typically lower than the average density of the planet. In the inner system, crusts are typically silicate-based, while in the outer systems crusts are generally icy. The thickness of the crust vary with tectonic activity. Plate tectonics indicate a thin crust.
COMPRESSED AND UNCOMPRESSED DENSITY:
The density question is complicated by the fact that planets due to their gravity compress materials. Thus a large world have a higher density than a small world even if their chemical composition is the same. In this document, it is the compressed density we refer to, for simplicity.
Icy planets, those made up to a significant degree of water ice, carbon dioxide, ammonia etc, are generally found only in the outer system. The building blocks of icy bodies don't condense close to the star. Icy bodies have very different tectonics than bodies made out of silicates and metals, volcanism may be in the form of gas geysers, large parts of the crust and even mantle could be molten by tidal stress. Impacts could melt large parts of the surface.
A system rich in heavy elements tend to have more and larger planets, in addition to a higher amount of heavy metals. Very old (poor) systems may have only gas giants and perhaps small icy worldlets, as no serious amount of material heavier than hydrogen and helium existed when the star formed.
The presence of radioactives in the core of planets provides internal energy to melt the core and generate tectonic activity. This is affected not only by how common radioactives are, but also the size of the planet. Large worlds have more volume compared to the surface to generate energy, and thus they stay active longer. System rich in radioactives may have been enriched by a nearby supernova explosion during formation.
These small worlds may have undergone little differentiation and thus may have little or no core/mantle/crust division. However, even the small chunks in the inner system has gone through some small heating. Larger chunks, like the large moons, always have some sort of differentiation and has had at least brief periods of activity during formation.
The process which forms the planetary system condenses matter at differing distances. In the outer system, ices are the norm mixed with some silicates. In the inner system, close to the star, elements like calcium, titanium, aluminium and radioactives, and many rare elements condense. Further out, iron metal and related minerals, and some non-metals like carbon and germanium condense. Even further out magnesium and silicon begin to condense (creating a large amount of silicates), and still a bit away sulphur, sodium and potassium begin to appear, mixed with iron oxides, pyroxenes and olivine. But this initial composition gets disturbed during planetary formation, when the planetesimals begin to collide and distribute the material more evenly.
Big impacts, orbital changes etc can all produce planetary bodies with different compositions.
Systems are rich (or poor) in various elements. This can be important. The systems that are poor in heavy elements (old systems) seldom form large planets terrestrial planets, as an example. But there are other variations that can be contemplated:
Carbon: In our system oxygen dominates over carbon, but some stars show an abundance of carbon instead. This will affect the system ... carbides and graphites will be common minerals. If metals are uncommon too, planets may be very alien to us.
Sulfur: Similarly, sulfur could be comparatively more common than silicon. Systems rich in sulfur will have different abundances of various minerals and compounds as hydrogen sulfide and sulfur dioxide.
Rare Elements: Some (rare) stars show an abundance of more exotic elements such as lithium (a light reactive metal), or even such comparatively uncommon metals as yttrium or vanadium.
Radioactives: Young systems enriched by supernovae can be rich in rare radioactive elements. Technetium, a rare light radioactive, has been discovered in abundance in certain C-class stars, for instance.
Noble Gasses: Neon and argon are two such gasses ... neon is common in the universe though not that common in our solar system. Noble gasses are chemically inert.
Different proportions of elements than in our system can be a potentially important factor not only for mineralogy, but also for native life.