As good as the games are you'll get burnt out playing through the whole series. People had years to go through them. Depending on your level of commitment I'd put it like this
Express: Yakuza 0, Yakuza 7
Low investment: Y0, Y1, Y6, Y7
Medium: Y0, Y Kiwami 1 and 2, Y6, Y7
Heavy: Play everything
I'm pretty sure all the games have recaps so you'll won't be completely lost. Yakuza 1 kind of a downgrade after 0 but if you finish 0 and wanna see what happens next it's no brainer.
Technically 7 is a new start, all you're really missing out on is not knowing certain people certain characters when you see them. Playing all these games might run you the rest of the year at least