There are so many Batman stories present in comics, and most of the Gotham characters are not new; they are from the comic world, except a few. So I am curious to know which storyline Gotham is faithful to.
It's going to be a bit hard to tell because Gotham has only had one episode, but I'd say, so far, that it's probably not really faithful to any particular story that's already been done. There will likely be homages or references, but so far it doesn't seem to be adhering to any particular story line, at least not strictly.
Edward Nigma, aka The Riddler, is shown to work as the coroner for the Gotham City Police Department. He's been depicted as a sort of private eye in the comics before, but never working directly for the GCPD in any capacity, especially not before his transformation into The Riddler.
Oswald Cobblepot, aka The Penguin, has been depicted as joining a gang only to be kicked out, but wasn't really the direct lackey of a crime boss. He was kicked out simply because they didn't like his appearance or mannerisms, not because he snitched to the police, and certainly not shown to be the subject of a mock execution by James Gordon.
The character of Ivy Pepper is likely intended to become Poison Ivy someday, but in the comics her name is actually Pamela Isley, and she's generally been depicted as growing up wealthy or middle class, not poor and the daughter of an ex-con.
The character of Sarah Essen is shown to be Gordon and Bullock's boss in Gotham. In the comics she's a love interest of Gordon, specifically after she was assigned to be his partner in the fantastic 4-part series
Batman: Year One(which is also where her character debuted). They have a brief affair, she relocates to New York to save face, but later the writers brought her back and Gordon even marries her.
The character of Fish Mooney is completely new to the franchise as far as I can tell.
As such, it's likely that it will draw on previous depictions of character's comic/story depictions while modifying them to suit the needs of the show, or possibly even changing them completely.
However, until more episodes are shown and we have a grander scope of the story and characters and their personal stories tied in with it, it's honestly a bit hard to say with just the pilot episode.
Short answer, it is a stand alone story that draws inpiration from franchise as a whole.