So, what are Fire-types, really?
The Purpose of the Fire Type:
As previously discussed, Fire-types are traditionally offense oriented. Predominantly Special, but also Physical as well. This means that, of all the types a trainer can get early, Fire-types are the easiest way to overpower most of the opponents, as there is no other type can be effective in both grounds besides Electric and Flying early in the game. As those tend to be weaker or more Speed oriented, Fire-type covers the role of a "stallbreaker" in the early game.
This is why incidentally the first two gyms in the first games are Rock and Water, as you most likely have already decimated the Rattatas and Caterpies and Oddishes. While this doesn't make the Fire-type easiest type to use, it makes it the most rewarding one to use in-game, as you can clear most of the game easily.
The competitive role of Fire-type is fairly similar, though it often involves some sort of set up, like Sunny Day, stat raise, or WoW spam. Similarly in the Doubles, the Fire-types are about spamming Lava Plume and Heat Wave to wear down the opponent.
In the late-game, however, Fire-types become a one trick pony, as the only two types they are effective against exist, Ice and Steel, the worst and the best types respectively. The rest of types like Dragon can easily trash them, though they can still deal some damage.
Because of this, Fire-types are generally encountered in three areas, Middle of the early game(around third gym), late mid-game(around sixth gym) and early mid-game(around fourth gym), as they are effectively irrelevant late-game. Nobody remembers Heatmor in BW Victory Road. This has caused the bulk of the non-Larvesta/Growlithe Fire-types to have around 480-500 BST.
The Aesthetic Archetypes of Fire Types:
Conceptually, the Fire-types can be divided into three, possibly four groups:
Generally composed of generic animals with flames surrounding them, these Pokémon are generally found in burned areas like Burned Tower and Pokémon Mansion, or plain routes. These Pokémon tend to have abilities like Flash Fire and Flame Body.
Generally composed of generic animals with colors traditionally associated Fire-type, these Pokémon generally don't have actively burning parts, or their burning parts are negligible. They might have patterns and design elements representing fire or have parts that only periodically burn.
Generally composed of magma, have magma patterns or some sort of smoke combustion area, these Pokémon are more specific than the other two, as they tend to be more Defense oriented and have Earth type moves(Ground, Rock, Steel, Fighting). They also tend to have abilities like White Smoke and Magma Armor, in addition to Flame Body and Flash Fire.
Generally sharing traditional appearances of other Fire-types, these tend to have either items that burn instead of them, or have a more blueish colored fire. These tend to be Special oriented with some access to paranormal types like Dragon, Fairy, Psychic or Dark.
The In-game Archetypes of Fire Types:
As discussed before, the Fire-types appear in only three major locations. This means that for each major location, there tends to be one archetype.
Regional Fire: As discussed before, one of the places Fire-types can appear is early-game. Like other main elemental types, Fire-types have their own regional variants. However, unlike other types, for certain regions, a previous Fire-type has been reused.
The rough outline of regional fires are like this:
GS: Same as above.
Regional early mid-game fire: This region generally contains species you must evolve to get their final evolution, and Magmar in GSC. These tend to be available after the regional fire.
Regional late mid-game fire: This region generally contains species you don't have to evolve to get their final stage, because they already are in that stage.
XY: Heatmor, again.
The Stat Archetypes of Fire Types:
The stats of Fire-types tend to go in following forms:
Dual offensive (slow):Generally one stat is around 120 and other is around 90. This Pokémon gets moves from both sides, but tends to be not amazing in either. They tend to be either wall breakers, or need some sort of stat buff. Notable examples include Emboar and Camerupt.
Defensive: Generally focusing on Physical Defense and Special Offense, the defensive variants tend to be about status spam. They are generally unused. Notable examples include Turtonator and Torkoal
Dual offensive (fast): Generally the speed surpasses both stats. They tend to need to boost one stat in particular, as otherwise they cannot dish mush pain. Notable examples include Infernape and Talonflame.
Tankie: Generally focused on mono offense with usable other offense, these Pokémon tend to have similar defenses in both sides. They either spam status or are focused on revenge killing. Notable examples include Heatran and Arcanine.
Mono oriented(fast): Focused on one specific type of offense, these tend focus on Speed and that offense. Nonetheless, they tend to have some level of all around stats and large offensive movepool from the other side. Notable examples include Salazzle and Charizard.
Mono oriented(stat buffer): Same as above, but these tend to have high defense of their respective stat. Examples include Volcarona and Delphox.