Now I've research what a game-ready character is, I need to start looking into the production side of things. One of the most important parts of a character project is deciding on your limitations (characters specs) so you stick within what your game can handle.
My mentor Mike Pickton said that it would depend on the character density in a game. For instance, with fighting games you might be 1 Vs 1 (Tekken, Street Fighter, etc.) or a large mob-based game (Dynasty Warriors, Vindictus); the less character's and tri-count heavy assets you'll have on screen, the more tris you can give to individual assets, which is backed up by the comment I found on the Unreal Engine forum below.
"The answer is "depends" it's been said before and will again but it all depends on your game e.g. amount of characters' weapons vehicles on screen. Now if you have 100 characters on screen then I doubt them being 30k would be a good idea but if you're only going to have say 5 then why not push a little higher. it all depends on what hardware you want to target and when". - Geodav, Unreal Engine Forum [1]
I know that often larger tri-counts are given to main characters because they have the most screen time, but it also differs based on the level of realism in your game. For instance, a highly realistic game like Star Wars Battlefront [2] will need higher poly character than a highly stylised game like Firewatch [3]. I'm shooting for semi-realistic characters and will go for a mid-range.
Another element that effects your tri-count is your end platform; next-gen consoles and high spec PCs can take larger tri-counts, whereas games meant for hand-held consoles and mobiles won't be able to handle and process too many.
Many companies optimise their games (adjust tri-count and effects) to fit their platform and make sure the game runs at least at a smooth 30FPS. You also don't want the game to crash constantly due to overload, as this would make the game unplayable and a bad product/not viable.
Character tri-counts from games (main characters):
The Order 1886: 100k
Infamous Second Son: 120k
Ryse Son of Rome: 85k
Sunset Overdrive: 40k
D4: 41k
Alan Wake: 13.4k
Asura's Wrath: 23k
Batman: Arkham City: 19k
Bayonetta: 23k
Blade & Soul: 10k
Borderlands 2: 13.8k
Bulletstorm: 17k
Devil May Cry: DmC: 20.7k
Witcher 2: 31k
Beyond Two Souls: 30k
Overwatch: 30k
Uncharted 2: 37k

From what you can see games can have vastly different tri-counts, but the main correlation for the higher ones are that they're realistic next gen games. The stronger consoles are able to take more and main characters get the most tris because they have the most screen time.
The level of realism effects the tri-count because they need to capture more details to make the models believable, and stylised characters rely on strong primitive shapes to sell their personality -thus needing less tris.
I'll use this information to decide how many tris I want to allocate to my characters.
Bibliography
[1] GEODAV. (2014) Recommended polycount for player models and weapons. [Online forum] Available from: https://forums.unrealengine.com/showthread.php?18120-Recommended-poly-count-for-player-models-and-weapons [Accessed 16/11/16].
[2] EA DICE (2015) Star Wars Battlefront. [Origin] Microsoft Windows. North America: Electronic Arts
[3] CAMPO SANTO (2016) Firewatch. [Steam] Microsoft Windows. North America: CAMP SANTO and PANIC INC.
[4] POLYCOUNT. (2014) Polycounts in next gen games thread! [Online forum] Available from: http://polycount.com/discussion/141061/polycounts-in-next-gen-games-thread [Accessed 16/11/16].
[5] POLYCOUNT. (2013) Triangle counts for assets from various videogames. [Online forum] Available from: http://polycount.com/discussion/126662/triangle-counts-for-assets-from-various-videogames [Accessed 16/11/16].
[6] NEOGAF. (2013) inFamous: Second Son Characters Polygon Count revealed. (120k Polygons) [Online forum] Available from: http://www.neogaf.com/forum/showthread.php?p=108172593 [Accessed 16/11/16].
[7] GOSUGAMERS. (2016) Interesting insight into Overwatch Tech Art. [Online forum] Available from: http://www.gosugamers.net/overwatch/news/35188-interesting-insight-into-overwatch-tech-art [Accessed 16/11/16].