100% 0.Its fantastic and set prior to 1.Also they implemented small nods to 0 in the remake of Kiwami 1. Kiwami is much smaller in scope than 0 and the story isn't as good, but still thoroughly enjoyable, just a heads up!
I would say that Kiwami is enjoyable as a Yakuza fan invested in the world and story of Yakuza but wouldn't recommend it to a newcomer as it feels outdated and lacks much of the content and quality of other titles that makes up for that outdated feel. Definitely start with zero, there's a reason why we heard so much about the game but not so much about Kiwami.
*sigh*
Complete and utter fallacy.
Story isn't as good? Subjective. 1's story is still probably the best in the entire series. Just because there is a large emotional aspect to 0's story, doesn't make it "amazing." Its good, VERY good (every game in the series has a great story), but there are a few issues here and there and the plot lags for the majority of the midgame (not my opinion either; the rise and fall of plot situations/devices is not used to great effect, hence the lag).
1 is Kiryu's defining story of all the games; it is brilliant, sets the tone and foundation for the rest of the series and Hase used a proper plot flow with writing, devices and characters, that makes the story brilliant, cohesive and focal. The only other story in the series like this, is 3, but that has a few lagging moments that take some luster out of the brilliant moments.
As for being smaller in scope/"outdated," this is a restored/remade version of the first title in the series, which was:
1. The shortest title in terms of playtime
2. The one with the least amount of features
3. Has a ton of, "early installment weirdness," that later titles would either refine or do without.
Thus, of course it'll be smaller in scope: you can't add 15 hours to a game without completely overhauling almost everything (like REmake).
Anyways, chronologically, it would be best to play them like this:
0, Kiwami, Kiwami 2, Kurohyo: Shinso, 3, Kenzan!, 4, Dead Souls, Kurohyo: Ashura Hen, 5, Ishin!, Hokuto ga Gotoku, 6
That's just my opinion, but it provides a nice bookend for the series as a whole, as well as Kiryu's beginning and end, plus a nice evolution for the series, plot-wise.
EDIT** BTW, the, "small nods to 0," should be reversed; 1 came before 0, not the other way around.