Even in Zack Snyder's Man of Steel, Batman v Superman: Dawn of Justice, and Justice League, which skewed darker than any previous Superman movie ever had before, the character was someone who seeks to be kind. The world reacts in various ways but, at his core, "Clark Kent" is a compassionate, altruistic "human."
Unlike his co-star in the latter two films, Batman, most of Superman's films are relatively family-friendly. Tim Burton's two installments with that character are excellent but intense, the same which could be said of Nolan's trilogy. The DCEU installments have been a mixed bag, but they too are dark, and actually manage to become not just some of the Dark Knight's darkest installments to date, but the Man of Steel's as well.
Batman v Superman: Dawn Of Justice (2016)
Snyder had brought a slightly grimmer worldview to the table in Man of Steel, and in Batman v Superman: Dawn of Justice, the director attempted to understand the Man (for better or worse). It's also a film that has Holly Hunter's likable June Finch, a fictional senator from Kentucky, have her big moment in court interrupted via a jar of peach tea (actually urine) and an explosive device in a wheelchair.
Batman v Superman effectively opens with Man of Steel's most traumatic sequence, and the film never really lets up from there. Like Man of Steel, Batman v Superman has world-ending stakes, but the latter has less issue informing audiences of the fact that a beloved character can, in fact, die. There's also more bloodletting than in any other film of the franchise, particularly in one of the film's Lois Lane-focused early scenes. Batman v Superman: Dawn of Justice is grim and feels as such for the viewer, regardless of age.
Zack Snyder's Justice League (2021)
Zack Snyder's Justice League was part a historic level of fan service, part a (successful) attempt at fixing a broken theatrical feature, and part Snyder magnum opus. The third chapter of what would have ultimately been a five-movie story from Snyder, Justice League was larger in scope than both Batman v Superman and Man of Steel.
This includes plenty of violence that wasn't in Joss Whedon's theatrical cut (which should arguably be skipped altogether) as well as some harsher language. But if the viewer has seen the Director's Cut of Batman v Superman: Dawn of Justice, they can handle Zack Snyder's Justice League.
Man Of Steel (2013)
Certainly one of the most quotable Superman movies, Man of Steel is a product placement-laden joy from front to center to back. Its reputation isn't the best, but it's the most accessible Superman film to date. It doesn't nail every aspect of the character's core, but it gets the gist and tries to create something new.
With that being said, everything from the Smallville fight to the third act's World Engine is intense. The latter generated controversy and is riddled with scenes like Laurence Fishburne's Perry holding one of his helpless employees, refusing to leave her as she's trapped under rubble, as they await imminent death. That outcome is avoided, but it's a long and intense sequence that culminates in Superman snapping the victim's neck.
Superman (1978)
The original four Superman films are decidedly less serious in tone than Snyder's reboot, but it's not as if Superman has a live-action Krypto. The late director Richard Donner was able to deliver successful, memorable films in just about every genre and for just about every demographic.
But before he was directing Lethal Weapon or The Goonies, Donner was directing beloved icon Christopher Reeve as the Man of Steel in a film that's a bit long and complex for young kids. By the same token, it contains nothing truly inappropriate that should bar them from the screening room. With that being said, there is a naked little boy (Kal-El just after landing on Earth), which alone is probably enough to make the first Reeve Superman the most "inappropriate" installment.
Superman III (1983)
If the nudity in Superman doesn't bother parents, the scary scenes in Superman III might. There's also Richard Pryor, but he's so tamed down he's rendered virtually unfunny. Most of the film itself is just a forgettable version of the first two, and not even gimmicky casting helps make it memorable.
But it's also the movie where Superman turns bad. The special effects are extremely dated, naturally, but the very concept of him turning evil could prove overwhelming to his youngest fans. Of course, if they've seen him nearly do the same in either edition of Justice League, they'll be just fine with Superman III.
Superman Returns (2006)
Superman Returns was directed by Bryan Singer and starred Kevin Spacey (who becomes a poor man's Gene Hackman as Lex Luthor), yet it in and of itself is a fairly timid, innocuous time at the movies. Returns is a continuation of the Reeve era, and it's an ambitious concept that's only pulled off moderately well, but it carries over those four films' universally accessible tone.
The highlight of the film (Save for a supporting performance from Parker Posey) is Superman himself: Brandon Routh. He's a likable lead and perfectly delivers Superman's most heroic lines. He captures the warmth that comprised the vast majority of what Reeve brought to his time in the role, and the blame for the film's financial failure shouldn't have ever been near getting put on Routh's shoulders.
Superman IV: The Quest For Peace (1987)
Superman IV: The Quest for Peace is the Batman & Robin of the Superman franchise. So, on one hand, it's effectively unwatchable and widely considered one of the worst movie sequels of all time.
On the other hand, it's a film with an extremely cartoonish tone. Everything outside of that is Reeve's (technically, Superman's) series of speeches on the dangerous seeming inevitability of nuclear war. It's heavy-handed stuff, and the heavy-handedness is going to be more boring to the kids, which is one more reason to probably just skip The Quest for Peace on movie night.
Superman II (1980)
Superman II had a troubled production, with Superman: The Movie's Richard Donner taken away from the project midway through its construction, only to have Richard Lester brought in, who would go on to direct Superman III. The Richard Donner Cut (released in 2006) is the go-to version, without a doubt, but both versions are of a comparable level of appropriateness for kids.
Superman II is just a joy, rather tame and accessible, and is one of the definitive early superhero films. The villains are more goofy than scary (but not too goofy) and the plot clicks at a far better pace than the 2.5 original Donner film. Superman II was Donner and Reeve becoming not just comfortable with the title character but familiar, and they both knew how to bring the character's most altruistic and relatable characters to the forefront.