I thought I'd write a post that responds to the "advice" part of the threat title.
The way I like to play RPGs is more-or-less as Eero Tuovinen explains
here:
1. One of the players is a gamemaster whose job it is to keep track of the backstory, frame scenes according to dramatic needs (that is, go where the action is) and provoke thematic moments . . . by introducing complications.
2. The rest of the players each have their own characters to play. They play their characters according to the advocacy role: the important part is that they naturally allow the character’s interests to come through based on what they imagine of the character’s nature and background. Then they let the other players know in certain terms what the character thinks and wants. . . .
3. The actual procedure of play is very simple: once the players have established concrete characters, situations and backstory in whatever manner a given game ascribes, the GM starts framing scenes for the player characters. Each scene is an interesting situation in relation to the premise of the setting or the character . . . The GM describes a situation that provokes choices on the part of the character. The player is ready for this, as he knows his character and the character’s needs, so he makes choices on the part of the character. This in turn leads to consequences as determined by the game’s rules. Story is an outcome of the process as choices lead to consequences which lead to further choices, until all outstanding issues have been resolved and the story naturally reaches an end.
4. The player’s task in these games is simple advocacy, which is not difficult once you have a firm character. . . . The GM might have more difficulty, as he needs to be able to reference the backstory, determine complications to introduce into the game, and figure out consequences.
In this sort of game, the "cooperative experience" comes from the fact that the players
genuinely play their PCs, and the GM
genuinely frames scenes by reference to dramatic need.
Some RPG systems are better for this style than others - eg because they are more likely to produce PCs with clear dramatic needs; or they have action resolution mechanics that make it easier to stay focused on what is really at stake in the game.
But before getting into the minutiae of any particular system, I think maybe the most important thing - especially on the GM side - is accepting the need to be genuine in framing scenes by reference to dramatic need, which will be established primarily by
the players. I think the biggest obstacle to the cooperative experience is the GM wanting to control the game, by deciding what counts as the "real" stakes of the game.
So I think concepts like "the plot", "the adventure", "sidequest" - all terminology which prioritises the GM's vision of the game over the players' - is the enemy of the cooperative experience.