As above, 0 if you're new to the franchise. It's basically the origins story of the series and will introduce you to all the key characters and, incidentally, it has one of the best storylines (Majima's arc in particular).
Chronologically, it's 0, Kiwami 1 and Kiwami 2 (those are remakes of 1 and 2 respectively but only K2 is on the new engine). The rest of the games haven't been remade.
The turn-based games I had my doubts about but they're super-fun and absolutely worth playing, though Infinite Wealth's story is very weak by the series' standards. It makes up for it, however, by being one of the most unapologetically fun games I've played in the last few years
I can also recommend Judgment, the spin-of series, there are two games and 1 in particular has a very strong storyline.