So, what are Psychic-types, really?
The Purpose of the Psychic Type:
Psychic-type originally was conceived as an ultimate type of sorts, specifically the ultimate Special type. This allowed Psychic-type to become one of the better offensive types in the game, if an individual species was oriented towards that. However, because it was overpowered, it was overnerfed back, and modern Psychic-type suffered a brief period of "gimmicky-ness", when Psychic-type's versatility was used as an excuse for creating a bunch bad Pokémon with large movepools, unique abilities but lack of power.
As time passed on though, Psychic's old legacy came back to a degree, and allowed Psychic to become one of the most common and versatile types in the game, and one of the primary types that is associated with Legendaries, alongside Dragon, Fairy and Steel. Psychic still lacks the power to become a true stallbreaker type, but as far as things go it is a decent stat buffing sweeper and utility type.
The Aesthetic Archetypes of Psychic Types:Psychic-type is generally associated with Purple and Pink, but many of the early species were actually Yellow and Green colored, and some of the newer species are Blue colored. There are Grey and White colored species as well. Aesthetically Psychic-type can be grouped into following groups:
The most common group of Psychics, these are psychic species that organic animals with psychic powers. They can be psionics, empaths, foretellers or telepaths, but they are generally regular animals, plants, birds and humanoids. Some are yokai based.
These are species that based on inorganic items that are either alive, or species that are shaped like inorganic items. They are generally in Mineral group, though some are Amorphous.
Fetus-like species, these represent the depictions of psychics as underdeveloped humans and animals with great mental power. They generally belong to Field egg group.
Species that are extraterrestrial in origin or design belong to this group. They are often in Mineral group.
Species that based off stage magicians, performers of sorts or stage espers, they are often in Human-Like group.
The In-game Archetypes of Psychic Types:
In-game archetypes of Psychic-types can be grouped into following groups:
Early-game Psychic-type, three staged: The archetypical Psychic-type, these are generally humanoid species that have base forms that are hard to catch and raise, but have decent power in their middle stages, or vice verse. They generally occur in odd generations and have 490-500 BST.
Early-game Psychic-type, two staged: The second most common Psychic-type, they often accompany the three-stage Psychic-type, and in even generations where there is no new three staged species, they are the early Psychic-type. They tend to be in 465-485 range.
Gimmick: Generally single species, they tend to be in 405-460 range. They tend to have unique types and abilities, but they are generally not too powerful.
Mid-game Psychic-type: Generally two staged, they are upgrades on early-game Psychic-types. They tend to be in 480-500 range, but some are in 520-530 range.
End-game Psychic-types exist, but are generally rare.
The Stat Archetypes for Psychic Types:
Bulky Offense: Conventional bulky offense species, in Psychic's case are more focused on offense.
Balanced: Species with little to no orientation towards one end or another, these species are focused on stat buffing to attempt sweep or defense.
Dual Screens: A variation of a dual wall, these species are defensive species that excel in both defenses but are lacking in HP, and are focused on using Reflect and Light Screen.
Barrier Mage: A variation of a wall, these defensive species have some Speed and offense to balance their defense. They are more focused on a death of thousand cuts approach than true defense.
Trickster: Psychic's variation of an annoyer, these speedy species have decent enough offense and defense to keep themselves covered.
Black Mage: Species with high offenses, good speed, these have mediocre defenses and are more focused on OHKOs.
Red Mage: A variation of bulky offense, these are species that excel in Special Attack, Special Defense and Speed, but are lacking in other areas.