I'm fairly new to the realm of table-top RPGs and I've only been playing for close to two years. However, I'm very familiar with RPGs and RP style gaming - in fact, that's exactly what drew me to D&D in the first place!
As a player I enjoy being part of a story, exploring my character's personality and backstory, all while engaging with and interacting with the world I'm in. I focus more-so on making sure my character's stats match up with their story. Personally, I don't care to min-max my stats, that would change who the character is! I also enjoy when a DM takes the time to allow players to shape the world by result of their actions (both good and bad); and when the DM rewards, encourages, and enjoys descriptions of actions - both in and out of combat.
Myself as a DM, I'm not a stickler for rules. They have the foundation upon which I build a world for my players to explore. Yes, I do follow rules to an extent, but only if they benefit the story. I home-brew and modify these to give my players a more dramatic and cinematic experience.