Yeah, there's a lot of catching up to do if you haven't played any of them yet. I started with 3 and then 4 back on the PS3. Unfortunately, my console died soon after and I never got a replacement so I didn't play 5, just watched a part of a playthrough on YT. I really wanted to run around fictional Nagoya and Sapporo:/
As amazing as those games are, I'd imagine you burning out on them if you attempted to play them all. They are pretty massive and full of content, it's just too much to digest and can get repetitive if you have six or so games to plow through
For example, I have around 160h in 0 alone and I still haven't finished due to all the distractions and hilarious sidequests. Y3 took me more than 100h (still not 100%) and I was on NG+ completing missed stuff in 4 at 90h when my PS3 died. I don't think there's a series I put more time in.
Starting with 0/Kiwami/6 and then grabbing Kiwami 2 when it releases in the West is a good choice IMO. Plus, there's a fair chance Kiwami 3 will come at some point. Of course, 3, 4 and 5 are fantastic if you have a PS3 but it's really a lot to digest for a newcomer. Still my favourite series overall and one of the most entertaining ever.
EDIT: Dead Souls is pants, no need to bother with it. 6 releases in March 2018 and there are rumours that Kiwami 2 is set for this December in Japan.