I played Like a Dragon with no background and it was a great experience. Really wacky in a satisfying way. Only grievance is there is ~10 hours of cut scenes to beat the game.
If you enjoy turn based rpgs, you really should give them a try. Infinite Wealth is especially good and you don't need to have played previous games to enjoy it. Not only do they do an amazing job of being funny or dramatic in all the right places, but there is such a wealth of content that you'll regularly get lost in side quests and minigames on your way to completing story tasks.
Infinite Wealth was a very fun game but it's honestly one of the worst stories they've written in the series with plot lines that were incoherent with the situation they've wrote themselves into. Not to mention the amount of time they spent on the Hawaii side of things having a very plain and unexciting wrap up. It's only redeeming points are all the numerous call backs to the earlier games which is lost if you don't play the earlier games.
I highly recommending playing in a modified release order.
Kiwami 1
Kiwami 2 (skip the Majima Saga for now)
3 - 5 (these don't age as well and the stories are quite a nose dive compared to the previous 2, so I think it's fine to skip them if the gameplay isn't really for you)
0
Kiwami 2's Majima Saga
6
7 (known as Like a Dragon in English)
Gaiden
Infinite Wealth
There's also Ishin which is fine to play anytime since it's a spinoff but it casts characters from the main games to play historical characters so there's a neat bit of irony if you know who the characters are in the first place. So playing it after 7 would be the best time.
And then if you still want more, Judgment and Lost Judgment takes place in the same world and use the same brawler style gameplay but follows a detective instead.
Did you start with the original Yakuza? Kiwami has a couple things that would feel odd to a newcomer if they don't play 0, and the only reason you're skipping Majima Saga here until later is because you moved 0. If you start with 0 then all the context needed for Kiwami 1's additions and Majima Saga are available.
Plus, to be fair, we have had a massive number of newcomers credit to 0. It's probably the favorite in the series now.
Yeah I really find that 0 is now the definitive series entry. Everything kind of only works if you start with 0 and do Kiwami now. It's also a much tighter and satisfying character progression for all involved.
I started with 0 and dropped it within an hour because it was moving so slow and the plot was written in a way which wasn't very interesting because I didn't really know the characters yet.
Didn't touch the series for another year before playing Kiwami 1 which hooked me in all the way in the order that I mentioned earlier.
0 is really good but I don't think I would find it to be as good and hard hitting as I experienced it without having played at least Kiwami 1 first.