Not a mechanic as such but I enjoy games with "controlled chaos". That is games with randomised boards, starting options, random input throughout, etc. with enough gameplay possibilities to mitigate all of it and have a good chance to win given enough skill.

No " right" moves at the beginning at the game and no ability to plan through the end. I like always adapting my strategy tp whatever the game throws at me.

I also don't care much for negative interaction where the main target of your action is to reduce points/resources of your opponent(s). It's not mechanically different from gaining points/resources but I find that the later makes for a more enjoyable game and people focusing more on maximizing their benefits rather than taking satisfying but ultimately suboptimal potshots at fellow players.

On a similar note mechanics which give secondary benefits to other players are always welcome.

As for the little rules, fully agreed. Keep your core rules focused and flexible enough to allow for emergent gameplay. Keep exceptions to a minimum. This will likely lead to a more abstracted theme but that's not necessarily a bad thing. Good abstractions streamline gameplay and let you focus on the remaining thematic elements better.