"Do I just pick the most advantageous option?" No, you pick the options that you can best defend if you are ever audited.
It's clear that there is often not a sharp dividing line between living one place or another, and all the items above are factors in determining the date you become a resident.
But you might consider this: when did you have a new postal address at which you would be able to receive mail, and when did you tell others that you had moved (i.e., friends, credit card companies, etc.)? So the question of renting vs buying and a number of other questions become irrelevant.
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