It is very difficult to take a topic such as "ghosts take over the city and three guys figure out a way to capture them" and make it genuinely believable, but Ghostbusters does just that. There is so much reality and humanity to it.
These dudes get fired from their cushy university jobs, so what better time could there be to throw caution to the wind and blow all of your money on an experiment you've been working on to harness phantoms in a storage container? That's the American dream (in some weird version of America).
They are average Joes. Despite being versed in ancient Sumerian texts, they talk like real people. They enjoy Chinese food and Miller Lights and Twinkies, and have fantasies about ghosts giving them sexual favors, and oh yeah and they just happen to be genius scientists.
And what happens when their ghostbusting works? They do what any bros would do and revel in their success. They hit up the nightclub for some dancing after they pack up some phantoms. They make poorly acted commercials and use gimmicky sales tactics just like any small business owners. They do interview shows where they get made fun of because... they are ghostbusters, so of course there will be dead Elvis jokes.
Basically, if ghosts took over a city, it would be New York and I would totally buy that these would be the guys to save the day.