How to make a new world per character in starbound

As of 1.0 stable, the Threat Level of a planet is directly related to the planetary biome of planet, not the character. The biome of a planet can be identified by the highlighted keywords in its description, while their threat level is identified by the "Threat" keyword.

• Tier 1 - Low - Iron - Barren¹, Asteroid Field, Lush
• Tier 2 - Moderate - Tungsten - Desert, Forest
• Tier 3 - Risky - Titanium - Ocean, Snow, Dry Grassland
• Tier 4 - Dangerous - Durasteel - Mutated, Jungle, Toxic
• Tier 5 - Extreme - Aegisalt, Ferozium, Violium - Frozen, Dark, Frigid Ocean
• Tier 6 - Inconceivable - Solarium - Magma, Volcanic, Scotched

¹ Barren planets do not have any ores on them
² All planets also have coal, copper, silver, gold, core fragment and diamond ores. These are not used as the primary material for most weapons and armor.

All enemies receive a damage multiplier based on the thread level of the planet they're on, so the same enemy species on a Scotched planet (Inconceivable threat) will do significantly more damage than one on a Lush planet (Low threat). Higher threat level planets will also require more EPP upgrades as their environments are less hospitable.

Planets with higher threat level contains higher tiered ores, inclusive of all lower tiered once - eg. a Mutated planet (Dangerous threat) will have Iron, Tungsten, Titanium and Durasteel ore. In general, you need the previous tier's armor and weaponry to explore planets of the next threat level, thus creating a natural progression system, not unlike that of Terraria.

The only way I know of to find a specific planet is to know its coordinates, and even that isn't guaranteed to work between updates. Seeing as how this is still early beta, I would advise not getting too attached to anything right now.