If your looking for a game, I know of a few and although I haven't played any of them, they are constantly recommended and generally known as great systems.
Most of you would have already heard of GURPS, a p&p rpg framework that allows you to play in basically any setting,
Another popular one is a classic for cyberpunk settings, the game cyberpunk (yup, it was pretty much a given)
Warhammer, as it is in one of the videos you posted
Shadowrun, is another cool cyberpunk one
There are some other generic frameworks but because of it's popularity, GURPS probably has you covered. Although, a popular game with an already established world with lots of quirk and charm like the ones stated above and D&D will probably fit your needs as a group the best. The different systems and worlds these types of games establish gives you a lot to explore in the ways of creating a character unique to you and giving you a unique experience that you could only have with those unique systems in tandem with their setting.