If you want to play Mass Effect as a straight-up cover shooter, Soldier is the Class to go for.
That said, they struggle if a gun can't solve an issue, so remember to use biotic and tech-focused Squad Mates to balance out these shortcomings. Soldiers are also the only class to start with Assault Rifles in the first two games. The Soldier Class is the most approachable, able to use almost any weapon and absorb a lot of damage through health and armor, and have Powers that boost their health and firepower.
This allows you to take advantage of the various changes and additions to combat with each Mass Effect game, detailed at the bottom of this page in the Game-Specific Mechanics section. It's well worth noting that when importing the save of a previous game to continue the story, you're able to choose a different Class for that Shepard.