I haven't played Kiwami, but no way any one should miss out on playing Yakuza 1 (first time or otherwise), one of the best games in the series in terms of story (tie for me with Yakuza 4). It's also been about 10 years since its released, I really can't wait to see what it looks like on PS4 (hopefully improved on the Yakuza 1&2 HD version). Funny that the core structure of the game remains largely unchanged.
Also, I just ordered Yakuza Ishin! (and preordered DQVIII). A very expensive January which may include a preorder for Nioh later too. I now have all the Yakuza games except for the PSP ones. (Are they available on the PS Vita shop, that would be a hassle to switch memory cards and PSN shop region, but at least it would be doable sometime down the track should I run out of Yakuza games.)
Dang, they are still available on Play-Asia, $45 and $50 respectively. Guess I'm skipping them for now.. but that is awesome that PSP games are still available in 2017.
EDIT: There is a 'PSP the best' version available for $25 and $45 respectively. Makes the first game reasonably cheap to get.