Yakuza isn't necessarily the hardest game to get into, after all most games are numbered, but the franchise is still a large commitment.
So I decided to separate some games that I consider to be the best (or not) starting points for anyone who wants to get into the Like a Dragon/Yakuza franchise.

This is entirely subjective but I hope to guide newcomers into starting with what's probably the best.
So without further ado, let's go!

Don't Start With: Yakuza 0

This is likely going to be controversial for some of you. Why not start with the game that takes place before everything else? Why not start with the one numbered before everything else?

It's quite simple: 0 is supposed to be enjoyed by those who already know a bit about the franchise. Who can understand its references and who can truly appreciate the character growth of these characters.

Seeing the Mad Dog of Shimano, Goro Majima acting in a certain way for over 6 games and then seeing how he got to that point is way better than going at it chronologically. Because the surprise is actually worth it like this.

Time and time again I've seen people pick up 0, beat it, and then never play another game in the franchise.
It's just not the best game to start with - even if it is an absolutely amazing game, one of the best in the franchise even.

Absolutely Don't Start With: Yakuza 1 (PS2)

Time hasn't really been kind to the first 2 (or 3) Yakuza titles.
It's clunky, they have content removed, and the western localization works more in favour of a good laughter than being an actual good localization.

I'm not saying to completely skip this one, but only play it once you're comfortable with the franchise and have already experienced Kiwami.
It's definitely a fun game for 2005, but it's not the best Yakuza can be, and while it's the first - it's most definitely not where you should start from.

That being said, it's definitely a worthy curiosity, and I have played it on the PS2 and the HD remasters of 1 and 2 for the Wii U. I had a good time, but I didn't have an excellent time.

Start Here! - Yakuza Kiwami

Likely one of the best ways to remake a game in modern history. Anyone who's been through this game and the original now knows what a "Kiwami treatment" is.

This is definitely the best place to start the series from. It's a complete remake of the first game. It plays better, it looks better, and it's structured better.
There is absolutely no reason to start this franchise through the PS2 and not through here.

And don't even get me started on Kiwami 2. Once you finish Kiwami 1, you'll have an even better time with what I consider to be the best game in the whole franchise - Kiwami 2.

Maybe Start Here??? - Yakuza: Like a Dragon

Like a Dragon was the first Yakuza game I played through completion. It wasn't my first Yakuza game, that honour goes to Kiwami 1 - but it's the first one that I cared to beat all the way through.

Did I miss lots of plot details? Yes.
Did I miss lots of references? Yeah.
Did I have fun? Absolutely.

Like a Dragon plays completely differently from the other Yakuza titles, with it being a (very silly) JRPG instead of a brawler. If you're not used to brawlers and prefer JRPGs, you might wanna start here. It'll cozy you up to the workings of the franchise and present a very interesting (albeit not so deep) battle system.

The story is also absolutely fantastic and even if there are callbacks to past games, you don't need to know the entirety of it all to grasp what's going on and to have fun.

Just be aware that this is likely the largest game in the franchise, being a JRPG and all, but that's not necessarily a bad thing, the more the merrier.

Does My Opinion Count Though?

I personally think it does. I have played all Like a Dragon titles with the exception of Kurohyou 1 and 2, Judgement and Lost Judgement.
But soon enough that'll be fixed.
However, I consider myself a pretty big connoisseur of the mainline titles, and I can say without a shadow of a doubt that Kiwami is the best Yakuza game to start with.
After Kiwami just go from there to Kiwami 2 and then the normal numbered entries. I'd say 0 can safely be enjoyed after you play all mainline titles or at least after 5.

Don't take what I say as gospel however. If you want to start with I don't effin know, 3? That's on you. It won't be a good experience, and you will be left very confused, but I'm not your momma.
This is just my opinions and my opinions alone.

What really matters at the end of the day is that I spread the word of Ryu ga Gotoku, and make y'all play these titles, not because I'm a fanboy, but because no one deserves to miss out on all these incredible experiences (besides 3) before dying.

Anyway, that's it folks, thanks for reading, and have a good one!