The Starbound Universe is divided into 5 Sectors of space & character progression is divided into 10 tiers. While the Universe is clearly procedurally generated, there is currently no way to set the generation seed on your own system, everyone is playing in the same Universe. Sadly this means that the exploration aspect of the game can be very easily spoiled!

All Sectors include planets with these common ores: Coal, Copper, Silver.
All Sectors include planets with these uncommon ores: Gold, Platinum.
All Sectors include planets with this rare ore: Diamond.
Uncommon and Rare ore types are more common on higher tier planets.

Character Progression is divided into 10 tiers with corresponding metal ores or alloys:
Tier 1 = Iron
Tier 2 = Steel (Iron + Coal alloy)
Tier 3 = Titanium
Tier 4 = Durasteel (Titanium + Coal alloy)
Tier 5 = Aegisalt
Tier 6 = Ferozium (Aegisalt + Coal alloy)
Tier 7 = Cerulium
Tier 8 = Violium (Cerulium + Coal alloy)
Tier 9 = Rubium
Tier 10 = Impervium (Rubium + Coal alloy)

The Starbound Universe is divided into 5 Sectors of space: Alpha, Beta, Gamma, Delta & Sector X.
Player begins life in the Alpha Sector, the other sectors need to be unlocked through gameplay.
Sector X has leveled planets for the final 6 tiers of character progression.

Alpha & Beta Sectors have Iron Ore.
Alpha Sector has planets rated at level 1 difficulty.
Beta Sector has planets rated at level 2 difficulty.

Gamma & Delta Sectors have Titanium Ore.
Gamma Sector has planets rated at level 3 difficulty.
Delta Sector has planets rated at level 4 difficulty.

Sector X has planets rated at level 5 through 10 difficulty.
Sector X level 5 & 6 planets have Aegisalt & Uranium Ore.
Sector X level 7 & 8 planets have Cerulium, Plutonium & Uranium Ore.
Sector X level 9 & 10 planets have Rubium, Solarium, Plutonium & Uranium Ore.