I've only played a bit of Shenmue but I'd compare them to Yakuza.
The overall story to Shenmue is Ryu Hazkuki wants to kill Lan Di for killing his father. That said I guess you don't need to play the first game in order to understand the other two, I dunno how much context is missing. I think Shenmue 3 starts off with a remake of Shenmue 2 ending to allow some context with the mirrors.
You can get Shenmue I & II, III and it's DLCs on Steam (here's the
multipack).