he's next in line IMO...but not the "rightful" heir....I put his claim and Daenrys claim on equal footing at this pointWell, for one thing, he IS the rightful king. That's reason enough to follow him, I suppose. He's also the most meritocratic of the candidates: he doesn't care if you're low born or royalty, just that you do your job well.
He's also arguably the best military leader in the series, though the show hasn't done a good job to explain his role in Robert's Rebellion and the Greyjoy Rebellion yet.
And Davos was a low-born smuggler that became a landed knight serving Stannis, he has every reason to follow him. Specially considering that none of the other major lords (or kings) would treat him with respect and ignore his low-born origin to make him a top advisor.