I'd play 0, then Kiwami instead of the PS2 version of 1.
This is pretty much my plan but doesn't that leave me in sort of an awkward position for the rest until 6? I do own a PS2 and for some reason (despite me not ever playing the Yakuza series) I bought Yakuza 2 a couple years back. It's weird that it is finally gonna come in handy but I wish they were remaking 2... Then there are the PS3 ones which I do not own at all.