All Littlefinger wants is to watch the world burn.
Littlefinger wanted and still wants the love and affection of a certain woman who married a certain man who had his certain head removed by a certain sociopathic child born of incest.
More than anything, in the books at least, it appears Littlefinger's main objective, main psychological drive, is to be taken seriously, to be acknowledged as an equal. He wasn't an equal as a child. He wasn't an equal in King's Landing as the Court's moneychanger. He won't be equal until he accedes to power in the form of an honored family name. He now has the Vale, or is at least in the process of it. He's starting to acquire the lands necessary to be reckoned with.
He doesn't want to watch the world burn. He wants the world to bow before him and acknowledge him as every bit as good and powerful and strong as Brandon Stark.
That's my take, anyway.