The Nightmare Before Christmas Director and Star Discuss Prequel Ideas and More as Movie Turns 30 (Exclusive)

The Nightmare Before Christmas continues to enchant fans as the animated classic turns 30.

The hit movie musical is celebrating three decades since its release in theaters, when it wowed audiences for the first time with its unique stop-motion animation, Danny Elfman-fueled soundtrack and heartwarming story set against a spooky backdrop — one that the Walt Disney Company was originally hesitant to fully embrace, according to director Henry Selick (Coraline).

"There was very little merchandising at first, but then Disney realized the film's growing in popularity and they capitalized on that," Selick, 70, tells PEOPLE in honor of his film's milestone birthday. "And then finally, Disney called it a Disney film because originally, they were afraid it was too strange, it would damage their brand, and it was released as a Touchstone film." (Touchstone was a former label of Walt Disney Studios, founded and owned by The Walt Disney Company.)

But later, he says, "They embraced it and they took the Haunted Mansion [at Disneyland and Tokyo Disneyland] and, for Halloween, turned into a Nightmare Before Christmas thing. So it didn't seem to happen suddenly. It was just this steady growth, and then it ramped way up."

The movie, from a story by Tim Burton, follows Jack Skellington (Chris Sarandon, with the singing voice of Elfman, 70), the Pumpkin King of Halloween Town who dreams of something more and gets in over his head when he becomes obsessed with Christmas Town and recreating it in his home world. But with a little help from ragdoll Sally (Catherine O'Hara), he learns the importance of being true to one's self, and the real meaning of the Christmas spirit, friendship and love.

Selick, who made his directorial debut with Nightmare, says he "always" knew that Nightmare was a "f--- yeah project" for him, and that it originally started as an idea for a TV special that turned into something bigger.

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Speaking about his experience making the film, Sarandon, 81, recalls the challenge of voicing a character with "so many layers." "I was almost invariably working by myself," he shares of the long movie-making process.

"The only time I worked with anyone," says Sarandon, was with O'Hara, 69. "She and I spent, I think, a day doing the Jack and Sally scenes."

Despite being somewhat blind to how the final movie was going to turn out, Sarandon trusted the process because he had faith in Selick, who "knew what he was doing."

To this day, he's blown away by the "multi-generational" impact Nightmare has made, to the point where people still come up to him to tell him how much it means to them.

"A lot of young people come up to me and say, 'This was a movie that made me feel like I belonged,' because it was so strange and at the same time so beautiful, and its message was so positive," Sarandon says. "And as it turns out, they, in turn, now are watching it with their children."

In casting for the lead roles of Jack and Sally, Selick tells PEOPLE that Elfman, who composed the music for the film, "was always going to be Jack." But while "was phenomenal at singing," Selick says Elfman "just didn't really have the chops for the dialogue."

So when it came to finding someone for the Pumpkin King's speaking voice, Selick recalls feeling that Sarandon was a "phenomenal actor" whose "voice was close enough to Danny's that it could pass" as the same character.

As for O'Hara, Selick says that she was Burton's first choice for Sally. Burton, 65, had previously worked with the actress on 1988's Beetlejuice. (The two are also reuniting for the upcoming sequel, Beetlejuice 2.)

The filmmaker recalls that O'Hara "struggled a little more because of the oddity of" Sally, adding, "I'd say it was her biggest challenge ever, as a performer."

"She's an incredible comedian and there was nothing outwardly funny about the character," Selick says. "She's clever and sly and she's many things, but I had to work with her and she didn't like how many takes [it took] — I had to do a lot of takes to get her in the zone. But she did beautifully, and then she sang the song really well, 'Sally's Song.' She sang it beautifully."

The film runs a tight 76 minutes, but as Sarandon points out, "Every time you watch it, you see something new, because there's so many beautiful, first of all, visual components. And then there are also so many little visual jokes and so many visual interesting quirks, quirky characters who are not necessarily speaking characters, but who exist in this world."

Selick has spoken out in the past about how Burton incorrectly gets the director credit often for the movie, which is technically titled Tim Burton's The Nightmare Before Christmas.

And while it did "irk [him] a bit in the past," as he tells PEOPLE now, "it's not really a problem," as it is Burton's story and "for the most part, at least everyone in the industry, everyone in animation, knows it's me who directed it."

"I think it made sense to put his name on it to make sure people didn't confuse it, maybe with Nightmare on Elm Street or some out-and-out horror film. So yeah, it bothered me more years ago. It doesn't bother me at all now."

Asked whether he'd ever work again in the future with Burton, who was also a producer on the Selick-directed James and the Giant Peach (1996), Selick says, "I'd say it's all about the project, and yeah, absolutely."

"If it was the right project that we both had a passion for, no problem. I'd love to work with him again," the filmmaker adds.

As for a potential sequel, Selick says that the labor-intensive nature of the first film isn't what would make him hesitant to create a follow-up — rather, he thinks Nightmare is "a perfect movie [that] came out of the perfect time, only to grow into something far bigger over the years."

"I think Tim in particular feels like, why mess with that?" he adds. "He certainly doesn't need to make more money from a sequel. He has had so many other successes, and so far nobody's come up with a great idea for a sequel. And I still think that Tim gets to decide. I don't think there's any idea that would convince him."

That being said, "It might be more interesting to do a prequel," Selick says. "There might be a more interesting story there about how Jack became the King of Halloweentown."

Sarandon would "absolutely" be on board to reprise his speaking role of Jack should another movie come to fruition, as he still provides the character's voice for other media like video games, live shows and more.

"To quote Henry, 'F--- yeah,' " he tells PEOPLE. "If there were a sequel, I'd be there in a minute."

The Nightmare Before Christmas is available to stream on Disney+.