Where does a legitimized bastard fall in the line of succession? Like, if Jon Snow was legitimized as Ned’s son, where would he fall in the line to inherit Winterfell (so without any knowledge of him being a Targaryen)

Depends if we’re following Targaryen rules (which after the Blackfyre Rebellions put legitimized bastards dead last, even after women) or not. If not, Jon would have a fairly good claim as the oldest surviving “son.” If so, Jon comes after Sansa and Arya.