ok firstly im not an expert on wolverine's history, which in someways is probably a good thing but there are several aspects i think could follow on... I mean wolverine is a very complex character with many levels. I would say you could possibly straight Wolverine franchise as a trilogy detailing several Wolverine storylines...
So this is what it would do for a story... Guessing that by the end of this movie, wolverine's memory has been erased, and Sabretooth is left unknown what happend to him.
Act 1: Wolverine is fished out of an icey lake in Northern Alaska by some eskimos and is taken to there local village, Wolverine awakes with no memory of what has happend to him and decides to work in the village whilst he tries to regain his memory... However the village comes under threat by a drugs cartel who are transporting goods through the antartic to avoid detection. Leading this transfer is Silas Burr a former weapon x employee who used to work as a mutant tracker for stryker however when the facility was destroyed Silas became a enforcer for hire. When he discovers wolverines presence he believes that Stryker had sent him to bring him back. So Silas and his crew attack wolverine and destroy the village... after relising wolverine has no memory Silas retreats back to the ship heading to madipoor, after seeing the damage that has happend because of him wolverine leaves to track down Silas, knowing the ship was heading to madipoor he manages to catch up with the vessel and stows away on board. He learns that Silas is working for Kenuichio Harada - once business partner to William Stryker, now Business revivals, Harada tecnology designed the plastic technology which Stryker used to develope a device to hold Magneto. We find out that the drug Silas is transporting is actually a mutant power enhancer, which Harada is planning to use to create the ultimate soldier, - Since Stryker and Harada parted ways, knowing that Stryker was working on the ultimate soldier, Harada decided to create his own Weapon X... Wolverine confronts Silas who lets slip that Harada technology was used to wipe his memory, However Silas realises that wolverine still hasnt realised who he is so they ends up in a fight leading to wolverine managing to cause the boat to sink, Silas desperatly tries to save some of the mutant power enhancers but ends up injecting them into himself just before he sinks with the ship... Wolverine manages to escape via a lifeboat.
Act 2: It is days later, Wolverine ends up in Madipoor where Kenuichio Harada was planning to meet Silas at the drop off point. However learning that his ship did not make port because of Wolverine, Harada sends his best samuri ninja's to capture him...Harada knows who Wolverine is, and plans to warp his mind into becoming his own Weapon X, however Wolverine evades capture by the help of a detective Shiro Yoshida, who has been investigating Harada Industry, Shiro was at the port waiting for the ship to come in, Shiro is also a mutant to which he uses his powers to help him and wolverine escape. Whilst in hiding Shiro explains that his father used to work for Harada Industries but went missing, Shiro became a detective so that one day he can discover what happend to his father. He learns that Harada Industires had dealings with a group called Hydra where he managed to find information about the transport of this drug, Shiro is contacted by his sister who works as a office employee at Yashida Corporation, which is connected to the Harada Industry. she learns that Yashida has been funding a small training camp in Japan which was being converted into a Research Facility for Harada Industry. However Shiro's sister is discovered and is captured by Harada... knowing that wolverine is with her brother, he takes her to the training facility which leads to wolverine and shiro following.
Act 3: In Japan, they manage to break into the facility but we discover that Silas is still alive and is now super-powered now calling himself Cyber. They fight leading to wolverines capture, and Shiro imprisioned with his sister. Harada appears and tortures wolverine, however he plans to make wolverine his own ultimate weapon x, so He pits him and Cyber against each other with hunders of ninja soldiers fighting them both. The Mutant Performance Enhancher has made Cyber a controlable drone who seems to be using wolverine like a baseball bat to fight off ninja guards. Wolverine manages to change the tables causing the places to fall apart, Cyber gets trapped by the building which is falling apart, Wolverine manages to free Shiro and his sister who he tells to leave, but shiro after learning that Harada killed his father wont leave until he takes him down. Suddenly Harada appears from the reckage in Silver Samuri armour, Shiro goes to fight him but is knocked unconcious, then we have a fight between Silver Samuri and Wolverine which leads to wolverine knocking Harada unconcious, he leaves him to Shiro to take into the police. When asked where he is going to say hello to Hydra... leading on to a possible third movie were Wolverine would face Viper, Omega Red, before ending up back to canada to being approached by Department H and declining there offer.
Well as you can tell im not a hundred percent knowledgable about Wolverines past but i think this would make a good story.