So, what are Normal-types, really?
The Purpose of the Normal Type:
Normal-type was introduced for two major reasons, one was to have a non-elemental type that wouldn't be ???-type, and to have to type to physically oriented moves from Fighting-type. Normal-type effectively is the common terrestrial enemy type. As the franchise evolved, Normal-type became one of the major specially defensive types alongside Psychic, though this role was achieved largely by its small amount of defensive species and lack of a Special weakness.
In much later generations its specially oriented caliber was given the ability to abuse Sound-based moves, and while this remains, there are other, better species that Sound-based from other types, like Noivern, and Normal/Flying-types. The sole mono Normal-type with Sound-based moves is Exploud, and it is a one trick monster.
Its role as the early route enemy type was eventually covered by Dark-type and its role as a Special wall was eventually covered by Fairy-type, leaving Normal-type with its large HP. While Normal-type might seem like a good damage sponge, due to abundance of Fighting-types, inability to hurt Rock, Steel and Ghost-types, and its overall weakness in stats have lead Normal-type to ruin. Normal-type is probably the only type that has been milked enough to die.
The Aesthetic Archetypes of Normal Types:
Normal-types are generally given pastel colors. Prior to introduction of Fairy-types, Normal-type was associated with Pink, and remains to be but in a lesser manner. Its more commonly associated with Brown, Grey and White, however. Conceptually, the Normal-type can be divided into following groups:
Most Normal-types belong to this group. They are animalistic species with bestial moves. They occur primarily in Field, though part Flying ones occur in Flying. Some might appear in Monster, Human-Like, Fairy and Dragon in addition to this.
These consider Normal-type as the non-elemental type. They are artificial Pokémon that don't have mechanical parts enough to be considered Electric or Steel.
They are species that use Sound-based moves. They might also get some dancing moves.
They are either yokai or kaiju-based species with non-elemental preference. They generally have some association with regular animals, but enough to be completely based off them. They belong to Monster Egg Group, mostly exclusively.
Ditto, Regigigas and Arceus belong to their exclusive conceptual archetypes, mimic, non-elemental deity and creator deity respectively.
The In-game Archetypes of Normal Types:
Early regional birds will not be mentioned. Similarly, early Fairy-types will not be mentioned, as they no longer belong to Normal-type.
Early rodent: You know what it is. Going from 410-423 range, these are two stage Pokémon that based on rodents, common carnivores and lagomorphs. They tend to get Super Fang.
Early secondary Normal: The second earliest Normal-type you will encounter. Generally cat based and two staged, but can be anything really. The only three stager, Stoutland is 500 BST(though Slakoth and Whismur debatably also count). Rest are generally around 440-460 range.
Mid-game Normal: Generally one staged, they occur during the mid-game. They are generally not powerful, but they might have interesting typing and abilities.
Late-game Normal: Generally occuring around the last Gym and Victory Road, these are one of the last species you'll encounter in game. One-staged ones are around 490, and two staged ones are around 500.
Gimmick: A low stats species that exists for some specific gimmick. They generally occur late-mid-game.
The Stat Archetypes for Normal Types:
The Fat Blob: Originally an archetype exclusive to Normal-type, this is now partially shared with Fairy-type. These are species with decent defenses and good health to abuse it. They might have decent offences.
The Jack of All Trades: Basically balanced species with no expertise. Slower ones tend to focus on health.
The Annoyer: Fast species with access to status moves. They tend to be mediocre in other stats.
The Beatstick: Offensive species with great Attack or Special Attack but mediocre stats elsewhere. They might be bulky or speedy, but their stats are far too under specialized to mean anything.
The Bulky Offense: Species with lower HP and better defenses and offense, unlike Fat Blobs, these guys their bulk to help their low Speed.