I got into it for basically the same reason. Heard it was like GTA but in Japan, and a friend of mine recommended the series. So I started with Yakuza 3. Then I played 4 and 0. (Though I knew about some important details from Yakuza 1.)
Even though I had played other Yakuza games before, the story in 0 still surprised me.
I expected it to be good, and it was still better than I expected.
Facial animations are really really good, as they do facial captions of the actors. And they are real actors who look the same way irl. (Aside from the sixpacks. Not sure why every old man in Yakuza is ripped, but it's a thing.)
For mini games, have you encountered Nugget? I suggest checking out a side quest in the bowling alley if you haven't.
Oh yeah, and did I mention they used the real likeness of several well known porn actresses? The faces are crafted so perfectly I was able to recognize them long before I got their names. It's so much fun to watch them doing mundane work. Almost as if they are normal people with normal lives.
Fun fact, I hung out with one of those girls, as she was a friend of a friend. Super cool, went for food and drinks, talked about old fighting games. Didn't realize she was in a Yakuza game that I had played, until later on. (That's because in the version I played, they had removed the hostesses.) She's not a porn actress though, but a celebrity MC.
There's a reason why 2017 always comes up when people ask about the best year in gaming.
Breath of the Wild
And btw, Persona 5 and Nier are also very surprising games where you can easily misjudge the book by the cover.
Looking forward to your post game impressions.