Littlefinger is planning to marry Sansa with Harry. If he achieves that, then he hopes that they will listen to him and he'll be like a father figure considering that he made them together. The next part of the plan is to take North with the Vale knights which would be piss easy considering that most of the North Lords would join Sansa against the Boltons. He is on name the Lord of Trident (getting the title and Harrenhal), however Walter Frey is the most powerful Lord on that part of the world. But if he manages to control both the Vale and the North, then he could easily defeat Frey and pretty much in one way or another control the biggest part of Westeros, and be able to go against Tyrells and/or Dorne (by that stage the Lannisters are completely irrelevant). Considering that Martells and Tyrells hate each other, he could easily join forces with one to defeat the others and then defeat the last actor on the stage.
However, there are a few things which will make his perfect plan completely failing. Starting from Sansa being a Stark and getting smarter every day. While he is expecting the naive little girl, he will soon be surprised. Then, there are external actors (Aegon/JonCon and Daeneris) which he isn't expecting. And finally, there is Varys who is an even better player than him, and while Littlefinger thinks that he has put Westeros on war, he is just a decoy on Varys' plans.
Regardless that his plan is a great one, he won't be able to realize it and I will be surprised if he doesn't get killed (likely from Sansa) on the sixth book.
I don't think that there is any need for spoilers on speculation (according to OP). Just the images needs to be spoilered (Niall's orders).