G3.5?
I love to have a good story, but I like the story to arise out of the gameplay and interactions between players/characters, not to be forced upon the players by the DM (we've tried campaigns like the latter and they ended up going... poorly.) Emergent storytelling, you might say. But if the mechanics of the game suck, I can not stand to play. I will try, and I'll give a new system several months worth of opportunity to prove itself to me, as I did with 4th Edition (5-6 months trying it), but in the end the system and mechanics just got in the way of my enjoyment of the game and I had to stop for my own sanity; I just couldn't take anymore.
I enjoy role-playing and combat in equal measure, and to me a great game includes equal parts free-form role-playing and mechanical gaming/combat (I like to use the example of spending one entire session taking place in an intense dungeon crawl full of tooth-and-nail combat... and then the very next session we return to the city to spend some time recovering from our adventure and get invited to a grand ball to hobnob with the nobility and spin grand tales of our heroics, without a single die needing to be rolled the entire game session. For me that is nearly an ideal campaign paradigm.)
But I also feel a need to point out that, to me, role-playing and story-telling are two separate things. Related, but separate. Great role-playing can happen without any hint or need of over-arching plot or story, just as real history doesn't actually have any plot, just the interactions of many people creating a grand story that emerges from their interactions. Now, that isn't to say that stories shouldn't be happening around the PCs, or that the PCs enemies shouldn't have plots in motion... if there are stories happening in the background of the world, stories which the PCs crossover into and interact with from time to time, that is a fine thing and makes for a compelling campaign. But when the DM is trying to tell his own private "novel" and force the PCs into filling roles he has envisioned for them, that leads to very frustrated players who have lost agency and control of their own characters.
I enjoy role-playing as a simulation, as in I create a character who fits into the history and background of the world in which he lives, and then play him as logically as I can in accordance with the world and the character's history and backstory (and this is one reason why I love Backgrounds being written right into 5E as a game mechanic, actually determining some of your PC's skills and abilities, and the rules having personality traits and such with actual mechanical benefits to encourage other players to remember and portray such things about their own characters.) I try to play my PCs as real people as much as possible, fleshing them out in my head and giving them likes and dislike, preferred clothing styles, quirks, and long- and short-term goals so that I will know how they would react in any situation (ideally I try to create characters who fit into a setting so well that they could be easily mistaken for a character originally detailed in a sourcebook or novel written for the setting.) If this is a highly detailed setting like the 'Realms this means I will research everything I can about the history and nature of the character's homeland and surrounding area, or if it is a more loosely detailed setting like Greyhawk I will try to anchor the character to a known historical element of the setting, like a war or battle or a kingdom or established family or noble House, and incorporate details such as ethnic dress styles and the like (such as making a character from Keoland who belongs to House Neheli.)