The story is loosely based on the 4 part comic mini series of Wolverine going to Japan. He mentions in the comic he was a punk kid going to Japan, it was done by Frank Miller and Chris Claremont. Here in the anime instead of an evil ninja leader, Mariko's father is a Yakuza leader and is engaged to an evil gang leader.
If people are still wondering. Then this is the famous cover of that comic where the lines
"I’m Wolverine. I’m the best there is at what I do. But what I do isn’t very nice." came from.
Funny though in the opening and ending anime it hints Omega-Red at the OP and Logan fighting Sabertooth in the ending. Not sure if it's all flashbacks.
Yes Iam a comic geek and a Mervel/DC fan as well.
Also Mariko is hotter in the anime version
EDIT:
Long time no anime after Ironman. This one I'll watch. Also thanks to duckroll for having more info. Can we expect Silver Samurai?