I am a staunch supporter of the Starks, They are the most noble house in the entire realm and i hope they attain independence, they certainly dont care about the Iron Throne, what matters to them is their independence, and they are the most at risk when the white walkers attack due to their proximity to the great wall.
Actually Sansa seems to really want to sit on the Iron Throne, judging by her conversation with Littlefinger in the new episode

what about the no one option?
the white walkers may kick everyone's ass and there would be no one alive to be king, or another power may emerge
~snip~
no-one option is:
The Night King 7.00
Here is my theory - humans will fight against each other, they will be weak, winter will come and Night King will defeat them all. He is un-dead king with special abilities ffs! Who can compete with that?

And it is the end I would like to see

There are rumors that the White Walkers are coming for Jon Snow as there are theories that say that Jon Snow was the Prince who was promised to them 8000 years ago. The White Walkers had some kind of pact with the Starks that was broken by the Starks,because of which Brandon the builder from House Stark built the wall after the White Walkers returned to the north after losing the War of the Dawn,so that they couldn't come back and start a war again.
Yet again it's a rumor not sure if its going to happen.
This might be true in the books, but in series it has been shown that White Walkers are a superweapon created by Children of the Forest that went out of their control, so most likely that their motive is just purge the world from all living creatures.