I feel like Yakuza, maybe more than any other series, can be played out of order without any problems. I think I went 4, 3, 5, 1, 2, Dead Souls, 0, 6, with no real ill-effects. There are always going to be a few plot points you might not catch, but I can't think of any way playing a later game in the series will ruin an earlier one. The stories are so self-contained, and there's no real over-arching grand plan to keep track of.
I mean, think about 0 and 1. If you played 1/Kiwami first, then it's great going to 0 and seeing how Kiryu and Nishiki's relationship was back in the old days. If you play 0 first, then seeing how it all ends up in 1 makes it hit that much harder. It works either way. If you play 3 before 2, I think the only thing that'll change is that you'll meet Kaoru and think "Oh, she's that lady from the start of 3, I wonder what her deal is"; it's really not going to spoil anything.