Marvel Comics started out its life as Timely Comics, with the publication of Marvel Comics #1. Throughout World War II, the company had popular superhero properties with the Human Torch, Sub-Mariner, Captain America, and others. However, after the war ended and interest in superheroes waned, Timely moved on to other genres. They changed their name a few times through the Interrogenum, but the one attributed to the company at this time is Atlas Comics, as it was the most frequent.
Eventually, the company settled on the name "Marvel Comics", likely named after their first ever issue. Shortly after this change, they jumped back in force into the superhero genre, with the Stan Lee-written Fantastic Four #1 in 1961. In short order they were rivalling DC in sales, firmly becoming one of the "big two" comic book publishers.
Marvel's most popular characters don't date prior to 1961 for the most part, and unlike DC, it is hard to give a "big three" characters. Popular characters include Spider-Man, Wolverine, Captain America, and the Fantastic Four. The company has also been successful in movies, being the first company to create an interconnected movie superhero universe.