My go-to system for pulp adventures is Evil Hat’s Spirit of the Century. It’s based on their FATE system.
If you’re not used to FATE, it can be a big adjustment form more traditional role-playing games. It’s a much more narrative system, better suited to simulating genres and quick play than more mechanical systems.
The advantage to this is that it’s a lot easier to set up a quick encounter by using the aspects feature in FATE.
Aspects are just a quick means to describe a property of a place or person. This applies to everything in the game, including the PCs. Aspects can be physical, mental, or just genre-based. Anything that would affect the story.
If i need a band of cultists quickly, I can just say they have the aspects Fanatical Cultists, Protect Idol at All Costs, and Can only Fight in Packs. That’s all the information I need to run an encounter. (there are some other stats, but they’re quite simple to make up)
I can create a place quickly, by just listing a bunch of aspects – Shadowy Corners, Rickety Stairs, Crates of Weird Artifacts, etc.
I won’t go into details of how it all works, but the aspects aren’t just for flavor, they have an actual mechanical effect in the game. There’s a good intro at https://fate-srd.com/
The full Spirit of the Century rule set is at http://www.faterpg.com/dl/sotc-srd.html
The nice thing about SOTC is that it’s ridiculously easy to make up a scenario quickly. It’s specifically designed for “pick-up” play, so you can run a game with little preparation.
On the con side: FATE can take some getting used to, and it helps to have the special FATE dice, though ordinary six sided dice can be used.
SOTC is currently out of print as a paper version, but the PDF and E-book versions are still available.