Best way IMO is the PS4 titles first -
PS4 titles - Yakuza 0, Yakuza Kiwami (out this week), Yakuza 6 (March 2018), Yakuza 2 Kiwami (possibly 2018 for the west) and then
PS3 titles - Yakuza 3, 4, 5, Kenzan, Ishin, Dead Souls
This is because Yakuza 0 is probably the best title in the series and the Yakuza formula is far more modern and refined than the early PS2 titles.
If you want to play them in release order -
PS2 - Yakuza 1, 2
PS3 - Yakuza Kenzan, 3, 4, Dead Souls, 5
PS4 - Yakuza Ishin, 0, Kiwami, 6, Kiwami 2
This is also ok, but it'll take you ages to get to the more modern titles like Yakuza 0 and by that time you may be wondering why people love the series so much.
Kenzan, Ishin are historical samurai spinoffs featuring the same 'cast' in different roles, 'Kiwami' means extreme and are the remakes, Dead Souls is a 'zombie apocalypse' spin off.