Which Yakuza game is that? Looks great!
Never played a Yakuza game, would the title in this gif be a good starting point?
I started with that game (Yakuza 3) and fell in love with the franchise that way but it's definitely not the best starting point. The story of every Yakuza game is more or less self-contained but there are many returning characters and organizations. It will be more impactful if you know their background. The best way to play the series is in order from 0-6. Yakuza 1 & 2 were on the PS2 but also have modern remakes called Yakuza Kiwami and Yakuza Kiwami 2.
Yakuza 3 is also generally seen as one of the weaker games (still great though) while Yakuza 0 is often seen as the very best. So, the best order is to start with Yakuza 0 (Zero) and then Kiwami, Kiwami 2, 3, 4, 5, 6 in that order if you like the series enough to continue.
You also shouldn't feel that you need to play all of the games to finish some big overarching story spanning all games which will be resolved in the last, there isn't one. You can start with Zero and end with Zero and you will have a complete, self-contained game. Same goes for every entry.