It seems disingenuous to say "she just happens to cross paths with all these famous characters",
No, it's quite non-disingenuous since she
happens to just cross paths with stuff related to all those characters, even though
none of them have crossed paths with
each other in a long, long time. It's not the same as meeting a whole baseball team at once, it's more like if you were on a random journey across the entire nation, and you
just happened to cross paths with every member of the 1983 Los Angeles Dodgers team, except in Rey's case, she's not traversing a nation of 300 million people, but a galaxy of countless billions of people, yet happens to run into just the
right people.
Remember, she
happens to come across clues to lukes whereabouts, then
happens to come across the Millenium Falcon, then she
happens to cross paths with Han and Chewie, then she
happens to be given Luke's original light saber, by another person she meets at random, and then she meets Leia (which at least makes sense, as she was
looking for the rebels), who
happens to task her with finding Luke, for no
particular reason that she got personally tasked with that, though I guess you can rationalize it as Leia being aware that Rey is "strong with the force". But still ... to be personally tasked what is supposed to be the most important task in the galaxy after just
turning up out of nowhere with no credentials is pretty convenient.
Notice that people
didn't give luke special treatment. He gets help and stuff from Obi Wan Kenobi, however that's perfectly reasonable, because Obi Wan was tasked with watching over Luke and views him like a son, and mainly gives him stuff that's his inheritance. Everyone else treats Luke as lower than shit for the first movie. Luke for example was only "Red Five" in the Battle of Yavin. Having found the message, rescued Leia etc, didn't actually mean he was automatically given command of a squadron or anything - he had to prove himself in the actual battle before being trusted with more authority. Whereas Rey basically pulls the same thing and is immediately given the task of commanding the Millennium Falcon to fly to the edge of inhabited space, find Luke Skywalker and convince him to help the rebellion again.
^ This is an example of "mary sue" storytelling. Luke wasn't given the benefit of the doubt: he was allowed to pilot a fighter because they needed every pilot they could get, but wasn't given any special
rank or anything until he'd repeatedly proven his worth - but also note that most of the top rebel fighter pilots
died at the Battle of Yavin. Luke being a
squadron leader at the Battle of Hoth would be perfectly reasonable
even if he didn't personally destroy the Death Star. Merely being a survivor of the Battle of Yavin would have given him seniority.
Rey was singled out for her "specialness" over and over again, such as being personally charged with caring for luke's lightsaber by it's keeper, and personally given the special mission to find Luke by Leia. So we're expected to think that across the entire Rebel movement, there's no one person that Leia would trust with looking for Luke, other than some random unknown person she's never met before?