For the purpose of this AU, most of Wolverine's history is the same as X-Men Origins: Wolverine. He was born in Canada, fought in several wars, notable during World War II where he spent the majority of it fighting alongside Captain America. Eventually he ended up part of Weapon X. Instead of going around as a loner, he was soon picked up by SHIELD while still suffering extensive memory loss. Though reluctant to join, it was better than his other options and he ended up joining as Agent Logan, code named Wolverine. He became one of their most useful agents, involved in many of their more notable missions in his long career. After joining up with SHIELD, he was sometimes involved with incidents involving other heroes. He was sent in for one attempt to bring in the Hulk, but the encounter was inconclusive for both of them and Wolverine was extracted before more damage could be caused in their clash.
Although not personally interested in the Avengers initiative, he inevitably was teamed up with the heroes when the world was threatened by an alien threat. He was reunited with Steve Rogers, who remembered Logan from their days in World War II (which Logan had no memories of). Consequently he is considered a key member of the Avengers and his particular skill set was very useful to them.
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He MAY have some history with the X-Men or some of the X-Men or something, if that's something that's wanted.
Although not personally interested in the Avengers initiative, he inevitably was teamed up with the heroes when the world was threatened by an alien threat. He was reunited with Steve Rogers, who remembered Logan from their days in World War II (which Logan had no memories of). Consequently he is considered a key member of the Avengers and his particular skill set was very useful to them.
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He MAY have some history with the X-Men or some of the X-Men or something, if that's something that's wanted.