Luke Skywalker put in cameo appearances for the first few issues of the Marvel Star Wars comic that followed the adaptation of the film, finally returning for his first full comic adventure in issue 12, Doomworld! 
But even with all the characters in play, there was still the question of what to do with them. The Empire was obviously the main threat, but they couldn’t feature Darth Vader as the main villain. Vader popped in and out for a while, usually by way of chasing after the Star Warriors in near miss encounters. It took a while for Vader to learn the names of the rebels who blew up the Death Star and shot down his TIE fighter, so at first he was more of a peripheral villain.
Even after Vader is specifically dedicated to chasing down Luke and to a lesser degree Han, he still is mostly a political threat, rarely facing off against our heroes in direct encounters. That leaves them a lot of time to wander around finding new trouble to get into. In the early days of the Marvel comic they mostly squared off against generic smuggler types and found themselves fighting aliens in gladiator pits (which happens so often in science fiction that it’s become a staple of the genre). Han and Chewie were put in a space gladiator pit in both the comic and later on in the newspaper comic strip, so they know more than anybody how often that sort of thing can happen.
A couple of interesting stories to note would be issue 17: Crucible, by Archie Goodwin and Chris Claremont, and issue 24: Silent Drifting by Mary Jo Duffy. No matter what context can be applied in retrospect, these stories were awesome when I was a kid because any opportunity to get a glimpse of the Star Wars back story was exciting. Crucible was just a story about Luke’s past on Tatooine, which we already glimpsed in the comics adaptation and the novelization, so it wasn’t that new and different. Honestly speaking, Luke’s life on Tatooine was intended to be boring and uneventful, so it didn’t make for a riveting yarn.
Silent Drifting was much more exciting, especially if you’re like me and Obi-Wan Kenobi was your favorite Star Wars character. Because if Kenobi was your favorite character, you were dying to know what he was like back when he was a Jedi Knight. And that’s exactly what this story promised to deliver.
I was really excited about this story when I was a kid. Obi-Wan Kenobi was the first Star Wars action figure I can remember owning. My brother recently reminded me that I actually had Chewbacca first, but there’s a reason I don’t remember him as well. We lost him very early on to our universe’s version of the Death Star: My Dad’s lawnmower.
In the later days of the EU, stories like that were forbidden by Lucas Licensing so as not to interfere with the upcoming prequels, but in those days no one knew where Star Wars was headed. Stories could take you anywhere, and with no other properties to fill that void, the Marvel Star Wars comic was usually where those stories got told.
One interesting thing to note about Star Wars in those days is not just how limited the stories were because of how little was actually known about the saga and its future, but also how strictly they adhered to the visual archetypes of the characters. Leia always wore white (mostly the same white gown as in the movie) with her hair in those awkward buns, Luke was either in his Tatooine farm boy outfit or an X-wing flight suit, Han always in a white shirt and black vest. The stories may as well have been acted out with Kenner action figures, because the characters almost never deviated from the costumes they had been given in the film. It wasn’t until The Empire Strikes Back later demonstrated that the characters did indeed make different hair and costume choices that the artists took license to stray from the iconic representations of the characters and give them a little more flexibility.
The strict adherence to the imagery of the first film wasn’t limited to the way the characters were drawn. Writer Archie Goodwin did his best to create stories that were new to the Star Wars universe but familiar within its framework. The rebel base on Yavin was a consistent backdrop for stories even though logic suggested the rebels would be forced to flee once the Empire had learned of its location at the end of the film. Many of the early stories revolved around the Empire’s efforts to blockade and eventually attack the fourth moon of Yavin, leading up to a final showdown in issue 25: The Siege at Yavin.
Besides being the final impetus for the rebels’ flight from Yavin, this story is important because it introduces one of the prominent villains of the frontier era: Baron Orman Tagge. Obsessed with avenging himself against Darth Vader for blinding him, Baron Tagge has a plan to use his company’s resources to end the rebellion and shame Vader, thus swaying the Emperor’s favor and leaving Vader out in the cold. This plan mostly revolved around freeze rays developed and tested on Tatooine, forcing Luke and Han to return to the desert world to stop them, but we'll go into that stuff a little bit later.
 Doomworld was also the name given to the first collected trade paperback that Dark Horse put out when they began reprinting the original series in the 90’s.
 Both of those stories were penned by comic series/comic strip scribe Archie Goodwin, so blame him.