I might have a few suggestions, depending on how liberal you are with those requirements of yours. Really, it sounds like you're asking for a bit of an ideal game, so I'm not sure I can give you that.
One Way Heroics - It's a turn-based, roguelike-esque game where you're constantly on the run from encroaching darkness, defeating monsters and picking up loot on the way.
The mechanics aren't too heavy and the gameplay isn't too complicated, but with multiple classes it's easy to spend quite a lot of time with it. It can be broken into runs rather than a single continuous game, so it's easy to pick up and put down. The story mostly come from the various partner NPCs you can pick up on your runs, so it's rather light (but the epilogues are nice). The game has multiple difficulty options and things to unlock.
Westerado: Double Barreled - In this one you're looking for the man who killed your family and burned down your ranch. Genre-wise, I suppose I would describe it as a 2D action adventure, maybe?
Started life as a flash game until it was expanded into a full retail game. Fun and easy to pick up. Again, this is a game that's more separated into runs rather than a continuous game. The plot and story are fine, but not the main focus. They're there to facilitate the game. A little light on challenge, but the last fights actually can be pretty tough on your first time through. There's a fair amount of content to explore and endings to find, so it has more potential playtime than it might seem, at first.
FTL - You're the commander of a ship trying to on the run from hostile rebels. I guess I would call this one... a real-time RPG focused on ship-to-ship combat, but you can pause during battle at any time to issue orders and designate targets.
This isn't quite what you asked for since it has very little story, but it hits your other requirements so I thought I'd throw it in. You might already be familiar with this one. It describes itself as a "spaceship simulation roguelike-like." Once again, it can be broken into runs so it's easy to pick up and put down. Plenty of ships and ship configurations to unlock, and the procedural content makes it easy to sink a lot of time into it. You'll find plenty of challenge here.
Sorry if these don't meet your requirements, exactly. I realize they're all a little light on story. Still, you might find some of them interesting, and I can go into greater detail on any of them if you want.