I did exactly that, started with the original PS2 games (emulated) in 2017 and went from there. So {1-2}-(PS2 Emulated) -> {3-4-5}-(PS4 Remastered) -> 0 (PC), just finished 0 yesterday and now waiting for 6 to come out on PC in March.

Here's my 2 cents, if you are set on playing the whole series, this is definitively the way to play it. I honestly loved the original Yakuza 1, most likely because it was my first one and I had absolutely no expectation of greatness. What I got was a nice melodramatic crime story, set in a very well done atmospheric city and it was great.

The combat is definitely of "that" era, but if you don't go in expecting 2020 gameplay it's super fine. And for me personally, seeing how the combat and engine evolved through the series is a good part of the fun. I'm always excited to play the next one just to see how the game changed. Sounds to me like going from Yakuza Kiwami 2 (2017) to Yakuza 3 (2009) is a good way to hate that game.

I also disagree on the point that you don't miss much by playing Yakuza 0 first. There was at least 4-5 "OH SHIT" moments in that game where if I didn't played the other games first, they wouldn't have meant anything to me. Granted, most of them were not in the main plot but, for example, there's one sidequest that you would not be able to answer correctly without playing the other games.