The Yakuza series or Ryu Ga Gotaku (Roughly translated to Like a Dragon) features the same main protagonist in every release of the series, Kazuma Kiryu, dealing with his Yakuza life, or the links he once had. The games have pretty complicated plots and for the most, well made too, although once in a while, the main storyline always branches off to some offshoot storyline that makes little connection to the game's main story.
MadeMan and Soup mostly explained it, it's an action adventure with RPG elements such as leveling your character up to gain more moves and an inventory system where you can put on armour, food to restore health in battle and weapons such as umbrellas and pullers, although all do have their maximum set of usage (Some weapons can take 9 hits, some over 30) Experience to level up can come from almost everything, from successful dating a hostess (One of the game's main minigames) eating food, solving sidequests or just beating up thugs.
The combat is pretty simple, but usually the main aim is to get the blue bar to the maximum so Kazuma can use his heat move, with the effectiveness of the move depending on what you are using or near by. For example near the edge of a balcony? Kazuma will throw the guy off, have a fish head? Kazuma would whack them silly with it, there is an enemy on the ground and Kazuma is holding up a baddie? He will throw the other one on top of him etc. The battle system itself is pretty good with throws, several combos, but nothing deep like Virtua Fighter.
I'd consider Yakuza 3 an improvement in almost everyway to Yakuza 2, the battle system features more moves, the environment is slightly bigger and the world seems a lot more lively. The camera system was also changed from Yakuza 2 to Yakuza Kenzan which now puts the camera at the back of Kazuma, instead of a set place like the first two Yakuza. Also Yakuza 3 also added golf and fishing to the minigames you can play. The series also has some oddball scenes and fights to remind you that you are still playing a video game, but it’s best I don’t spoil these moments for you!
I think the PAL release only has the Collector's Edition as the only version available and it will be the RRP of any new video game, which is neat. It’s supposed to come with info that will explain the character's history with each other and how they are linked as well as the soundtrack for the game.
Anyway, even if you haven't played the first two, I would recommend you to get Yakuza 3 anyway!