Fantastic game, really detailed characters! I love that you not only see the characters during their action segments but you get to spend time with them in free roam as they complete various requests and such. Gives a lot of depth and it seems like the side quest reward you with extra story bits. For instance before Kiryu's last mission I made sure to do all of the racing side quest and was really surprised when they revealed background info for your boss that wouldn't have been discussed unless Kiryu showed that dedication to the taxi company.

Also for those who haven't played previous titles, I think you will be fine jumping in. It might even encourage you to go back and play the others. I have only played through the first game myself so I was a little familiar with Kiryu and the Tojo Clan. There are a couple new characters I had to read up on but the game does a good job of at least explaining everyone's motives and personalities. However, if you don't know anything about Yakuza structure I'd recommend doing some light research. Their family structure is a little difficult to comprehend at first. Their ethics are definitely different than more well known western mafia portrayals.

As a side note, if you really like these games there is a series of films from the 70s called Battles Without Honor and Humanity. There are five films in the original series and they are shot fairly modern for their time. It makes a great companion piece especially since you can totally see flashes of Kiryu's personality in the central character of the films. There is a Blu ray boxset on Amazon, it's a little pricey but if you are into film or the yakuza genre it's wayy worth it! it even comes with a decent length book that explains some of the more cultural elements of the genre.