The first (the novel), 1898, expedition was a scouting expedition using "appropriate technology" to make sure nothing came back and bit them.
The second (the radio show), 1938, expedition was a second scouting expedition and attempt to see if their beefed-up physiologies could handle the Terran biosphere. Nope. And the appearance of a bunch of super-powered and mystical heroes was a kick in the pants they didn't need. The rather amorphous basic Skrulls headquartered on Mars called for help from the shapechanging Skrull elite.
The one in the early 50s (the movie) was more of a full-scale assault, the way having been prepared by various shape-changing agents devaluing the super-powered population and learning how to cope with human bio-organisms.
Unfortunately they had a traitor, the hero who came to be known as the Martian Manhunter. A psychic mutant Skrull of tremendous power, he decided he had more in common with humanity and (1) changed sides and (2) rallied a lot of heroes who were either in hiding or just plain disgusted.
The result was a resurgence of super-powered activity and the eventual formation of the Justice League, which operated sub rosa until another invasion, the Appelaxians, brought them into the open.