Order A (actual recommendation): 0, K1, K2, 3, 4, 5, 6, 7, J, LJ
As noted by many, this is probably your best bet. There will be a downward bump in quality between K2 and 3, but you’ll soon get over it since 3 is so good anyway. Judgment and Lost Judgment are of course optional but you’ll want to play them anyway so visit those once you’re done with the main series. Visit other spin-offs once you’re done too.
Order B (connoisseur recommendation): 1, 2, 3, 4, DS, 5, 0, K1, 6, K2, J, 7, LJ
The originals on PS2 still hold up, and playing in order of release gives a smoother technological progression. Kiwami 1 & 2 (and soon Ishin!) vary enough from their source material that it’s worth experiencing the differences. Language barrier permitting, insert any of the spin-offs in their appropriate places too. I like Dead Souls, stupid as it is.
Playing 0 after 4 / 5 gives a very different perspective on the story and I love that it can be experienced in both contexts. You’ll get a “so THAT’S what happened!” moment whichever order you go with, either in 4 or 0, with a certain part of a certain character’s past explored over the course of multiple games. Super clever. See you in five years.