Inside five years Joffrey and Tommen have "accidents" and Myrcella is Queen with Petyr as King-Consort.
I'd think he'd be smarter than that. He'd space the accidents out over a longer period of time. Joffrey or Tommen might even be king for a short time before he dies. Marrying Myrcella would also be rather on the nose, not that he'd want to anyway since Sansa exists...
Hand of the King is probably just fine for Littlefinger. Robert isn't really interested in ruling so Littlefinger pretty much controls the entire country. As for Robert's successors, if Joffrey is too troublesome then he will get axed as in canon. Tomen is more controllable. If Tommen marries Margaery then Littlefinger is going to have to step back a bit, lest he garner suspicious looks. He's still the Hand of the King so he'll have to content himself with being the second most powerful man in Westeros. If he decides to be greedy and wants to become the number 1, then I don't see his reign lasting long.
Real question is what happens when the Others/Walkers and the dragon lady come. I think he'd try masterminding the demise of the dragons. Ie, trying to get an agent into Dany's camp and having it plant an extremely potent poison into the dragon's food or water supply. At least one of them will probably die. Also if we go by the show, then Dany has to be kept alive and Baelish has to make sure she fights the Others/Walkers first, as dragonfire is pretty much the only hope of winning the war. Hopefully at least one dragon dies in the process. Dany doing the heavy lifting of dealing with the Others/Walker menace would give her a lot of prestige. Maybe Littlefinger could enact a propaganda campaign? For her last dragon, a ballista is a no brainer. Just put it on a merchant ship sailing down a river or along the coast, concealed by a tarp, and then when it gets within range unveil it and fire. Done. (Hopefully the people manning it practiced a lot, because if they don't hit on the first try they're not going to get a second). Could have multiple ballistas on a ship, or maybe multiple ships to raise the chances of success.
If Baelish learns about Jon's true heritage (somehow), or learns that Brann can warg into other beings, then he could try utilizing them to get rid of the dragons. Ie, Jon baits the dragons into an ambush, or Brann wargs into a dragon and pilots it into an ambush.
