My very vague concept of a GF IV storyline would have Anthony embittered and stunned by the murder of Mary, along with feelings of guilt (since she was murdered after coming to watch him perform).

Anthony could finish law school (from the dialogue in the movie I inferred he was pretty close to graduating anyway) and THEN enter the family business as an apprentice to B.J. Harrison (whom we are led to believe is at least professionally competent).

But I think Anthony would probably already have a pretty good idea of what the 'family business' is, he is under no misconceptions, he has not bought Michael's snow job the way Mary had, so he would hardly be going in completely naive.

Although Michael would be temporarily shattered by Mary's murder, more than anything I think he would be convinced that there was no hope for him (or the family) to "get out clean," to really go legit, he was condemned beyond redemption, and he would return to serving as Vincent's consigliere as Vito had for him.