Yakuza 3 was decent, I enjoyed it quite a bit. But I bought it for really cheap, so it might have helped. Haven't played Yakuza 4 but I would gladly buy a digital version on PSN. Or skip it and go straight to 5 if the rumor is true.
Think of the combat as a 3D Streets of Rage or Final Fight. You go around smacking dudes and build up a special meter that can unleash power moves. There are weapons strewn about that you can pick up and beat the shit outta your opponents with.
Outside of battles, they are action adventure games with a Tokyo setting. You can run around and explore the whole city district and find sidequests and food shops and other places/exhibits/etc. that add to the authenticity. It is an absolute blast to explore because there is some truly wacky shit in these games.