I can definitely recommend FTL: Faster Than Light. I still play it after many years in the exact same way you describe, that is short sessions. t’s all based on battles that last minutes at most while part of an overall campaign. You can quit anytime, even during battle, and it will just saw the state. You can pause during battle to think as well.
it also has simple rules but with a lot of depth. You upgrade your ship from time to time and also get new weapons or defences. It actually sounds like a perfect fit for what you want. It’s cheap too.