A New Hope is where it all began. It's absence was the dam holding back untold trillions of tons of merchandise, novels, films and TV shows. If your kid likes fantasy, sci-fi, or both, then show them this film. The plot is simple: The Galactic Empire has an evil space station capable of blowing entire planets apart, which the Rebels must destroy. Luke Skywalker, Obi-Wan Kenobi, Han Solo, and Chewbacca go on a quest to destroy it and rescue Princess Leia, accompanied by the two lovable, bickering droids, C-3PO and R2-D2. Violence is definitely there: Blasterfights break out frequently in the film, with a large one in the beginning resulting in several Rebel soldiers dying (though no blood is shown). There is a fight with Lightsabers (laser swords) towards the end, with a main character dying. An alien is dismembered in the now-famous Mos Eisley Cantina, with the one example of blood in Star Wars history being shown. The Death Star blows up an Earth-like planet, and there is a large space dogfight at the end of the film, resulting in an Imperial space station exploding. Very mild language, mostly the occasional d--- and h--- (foul language is very rare in Star Wars as a whole, in fact). Leia briefly kisses Luke, but nothing more. One scene takes place in a cantina, where patrons drink unidentifiable beverages. Some aliens may be disturbing to younger viewers.
An important thing to note: Star Wars is HUGE! Be wary if your children see this, for they'll clamor to see the other five films, as well as the three coming out in a few years. They'll want the action figures, the video games, maybe an account with Star Wars: The Old Republic (currently free for the basics only with optional microtransactions, but they may not be ready for it. Read Commonsense's review for it, I've posted one as well) and Clone Wars Adventures (Again, free, but with microtransactions. Not too inappropriate). That's about it. May the Force be with you!