This is a series I`ve long been interested in but not sure where to start. Yakuza 1 seems to be a no brainer, but I don't have access to it or a PS2 presently. I wish there was a PSN port of this game and Yakuza 2. I have 4 & 5 on PS3 as part of prior PS+ free games previously, but I haven't played them because I figure Ill be missing out on the whole experience without 1 & 2.
Yakuza 1 remake just got announced for PS4 localization, so you could wait and start there.
While all Yakuza games are pretty self-contained(not really serialized) they do acknowledge the events, locations, and characters of prior games pretty heavily so it is best to play in order. But each game also features primers to watch that detail the events of earlier games to get you up to speed, so you could jump in anywhere really. But unless in a hurry, may as well hold off for Yakuza 1 PS4 next year.