Shadowrun looks very interesting. I'd be happy to give that a run, if you don't mind my being a complete newbie. I'd never even heard of the game, but it looks very interesting. And honestly, I generally do much better when there is already a setting established. Helps with the my-brain-hates-world-building thing.

I also find it is easier to find our footing when we incorporate some sort of disaster or survival element into the story straight-away. We could work that into the setting - post-apocalyptic, maybe. But even if it doesn't last long, and is just a quick emergency that we have to respond to, it skips the typical "lets just have our characters accidentally bump into each other and strike up a conversation." I'm a lot like you - if the thread feels forced, I don't enjoy it as much. If we place our characters in a tavern and have them start talking just because we need to get a story started, I think that's a bit too convenient. But I'm sure you've already thought of that! Your Shadowrun idea seems to have a fair element of danger.