One important thing to learn in Shin Megami Tensei Liberation Dx2 are the Archetypes of demons, and how that will impact the growth or development of your demons.
To start with, there are five colours which denote your demon's archetype. White, Red, Yellow, Purple and Teal, which relate to Common, Aragami, Protector, Psychic and Elementalist. Each of these are important to keep in mind before fusing demons.
The archetype of a demon will impact the Awaken Skills they will learn, changing their specific uses in battle.
White is essentially common, colourless. During demon fusions, white archetype demons will have their archetype overwritten by whatever demon they are being fused with. The white archetype also bears no special abilities.
During multi-fusions, all demons will be required to be white or common archetype.
Aragami, or red archetypes, are built for damage, and will learn offensive moves in order to destroy opponent demons. These are great for the early game where most demons can be dealt with simply by doing as much damage as possible.
The Protector, or yellow archetype will be best at keeping the rest of your party healthy. These demons can draw the attention of enemies and heal with moves such as Dia and Diarama, taking pressure off your other demons. You can also expect Protectors to boost the attacks of your other demons.
Psychic archetypes are purple, and the Awakened Skills they learn often include passive buffs. These demons will learn the kinds of skills that will, for example, allow them to do more fire damage to enemy demons. Make sure to double check the skills your demon is learning before giving them moves and using them in battle.
Elementalist demons are some of the most useful. You'll be able to spot which these are from their Teal archetype. These will give more complicated, situational moves which will prove to be incredibly useful long term and in PVP battles. Abilities such as Resist, Null, Repel and Drain will all prove to be great moves against larger, tougher bosses or in PVP battles that you really don't want to lose.
White or common archetypes can easily be gained by normal summons or by talking and negotiating with demons to have them join your party, but demons of other archetypes are more difficult to earn. If you want demons of other archetypes, your best option is to perform a superior summon.