Because of his presence in the North, I think Littlefinger will start with Jon Snow and Sansa. He needs power in the North for himself, and the only avenues to that power are through the two of them. The easiest path is for Littlefinger to divide and conquer. Indeed, he has already sown the seeds of doubt and jealousy in Sansa's mind. The look that he and Sansa exchange during Jon's ascension in Winterfell's great hall is extremely significant. While Sansa is somewhat pleased for Jon, she also feels she isn't getting the credit she deserves. It was through her actions that the northerner army was saved from certain defeat. She also believes herself to be the last trueborn child of Ned and Catelyn, and by rights, Winterfell should be hers. Littlefinger will continue to nurture that seed of jealousy if he can—attempting to drive Jon and Sansa apart. Despite his attempts, I think Baelish will ultimately find Sansa unwilling to move openly against her "half-brother."
If Sansa remains loyal to Jon, as seems likely, this leaves Littlefinger with really only a couple of options. He can either ingratiate himself with Jon as an advisor, he can abandon his Northern ambitions entirely and try to attach himself to a different leader, or he can try to eliminate Jon entirely. Baelish is quite capable of murder—and of manipulating others into doing the dirty work for him. Given his preference for remaining hidden, any attempt on Jon's life would be extremely risky for Littlefinger. Sansa has been around Baelish long enough that she would instantly recognize his complicity in any murder plot. So I find it most likely that Littlefinger will take the safe course, attempting to become Jon's advisor. He will present himself as invaluable because of his grasp of court politics and money—both of which are skills currently lacking in Jon's retinue.