In The Westing Game, who is Sam Westing after?

I don't believe that Sam Westing is "out to get" any particular person. He sets up an elaborate "game" and/or murder mystery in order to help him find an heir worthy of his fortune. In that regard, he's "after" the person that can solve his game. That turns out to be Turtle Wexler, and Westing seems pleased that she won.
I suppose the other thing that Westing is after is the good of all of his heirs and the people that are involved with the game. He went to great lengths to pair them with the person that would bring out the best in each member. Additionally, Westing is a philanthropist, and he invests in people. He pays for the education of Turtle Wexler to become a lawyer, and he pays for the education of other people too. They in turn have an attitude of "pay it forward" and pay for the education of somebody else. Ford pays for Chris's education. Finally, the end of the book shows that each member of the group finds great success in the area that they dreamed of. Restaurants do well, an Olympian is made, happy weddings occur, and so on, and Westing is happy for each of those people.