Good question!
Let me start by directing you to this essay here where I talk about how Jack Kirby and Stan Lee turned the Red Skull from a rather shaky pulp villain into a pretty damn good supervillain with a penchant for cigarette holders, giant Nazi robots, doomsday devices and improbable escapes.
They also gave him a rather interesting backstory in Tales of Suspense #66: Johann Schmidt was a penniless orphan, bullied and robbed because of his physical weakness, who couldn’t find regular employment (although as Steve Rogers points out, “my early years were no bed of roses, either”), who was working in a hotel when Hitler came into town, and the rest was destiny:

And that’s the core of the character – he is Hitler’s very own Nazi, his hand-crafted avatar of hate. But at the same time, you can see the personality defects – the self-hatred (especially centered around physical weakness), the adoration of power and strength, the “envy, the jealousy” – that would make him such an eager convert. In a way – and there’s a reason why they named him John Smith – he’s a perfect stand-in for any of “Hitler’s willing executioners.”
That’s what makes him such a good “dark mirror” for Steve Rogers – because the two of them have virtually identical backstories as poor, physically impaired orphans, but they reached such diametrically opposed ideological conclusions. Long before he volunteered for Project Rebirth, Steve Rogers had chosen the path of solidarity, and before Johann Schmidt got his mask/face, he chose the opposite. Hence why this moment works so well:

The Red Skull needs there to be some inherent, almost biological reason, why Steve Rogers succeeded where he failed, because otherwise he has no way of understanding his life. And it’s a big part of the reason why so many of his plans revolve around trying to break down Captain America – drive him crazy, take over his body, putting NYC in a bubble unless Cap gives in – to find that reason and overcome it.
That being said, one major mistake I think people make with the Red Skull is that they try to make him too smart (he’s not a Batman-level strategic genius – he’s a monologuer, a gloater, a fan of the easily-escaped-death-trap and the explosion-prone-giant-robot) or too powerful (the Cosmic Cube should always be something he’s reaching for, but which always slips between his fingers).