A few basic things, and then I'll get into more detail.
I reject utterly any notion that immersion is not worth pursuing, or that different mechanics and systems can't reliably contribute to it or detract from it. If I want to play a game without immersion, I have all manner of games that take less time and energy to play than TTRPGs do.
I reject
just as much the notion that metagaming is antithetical to roleplaying. It may hinder roleplaying
for some individuals, but there is no inherent oppositional conflict between them. Often, metagaming of certain types can aid roleplaying, by reminding the player of the frame of mind of their character, helping them not just project the kind of day they're having into their character's actions. This is especially true of meta resources and "scores" and such, like relationship scores, bonds, rivalries, obligations, debts, favors, etc.
The primary times that I don't want to think about mechanics is when I am in character, doing something that I do regularly in real life, and when that thing is not complex in a way that cannot be easily understood in the moment or cannot be modeled well without much structure.
I prefer not to have my players feel beholden to the 3 primary social skills in every situation. The Bard or Rogue or Warlock might be the party face in most situations, as charm really is quite effective in most situations, but the Fighter or Barbarian in my games can use the same check they'd use to see to their travel kit (Wisdom; Survival) to create a rapport with the King's Scout Captain, and explain the importance of what the Paladin is talking to the King about, gaining an ally (and a success in the skill challenge to get the King's support in expanding the network of watchtowers and ranger posts in the borderlands).
When I am roleplaying a social challenge, I generally only want mechanics for those things where my character's understanding is inherently different and separate from my own. Things like, the feel of a room of people, my character's ability to judge body language beyond the simple surface stuff, my character's in character knowledge about the nuances of a social structure very unlike the one in which I live, the thoughts and feelings of a character other than my own, etc.
So, all that established, the social mechanics I have used and enjoyed;
I like mechanics to build organizations.
- They help make the organization easier for player's to manage without detracting from play
- They help the DM use the organization to help the PCs and to challenge them
- They give a great alternative to the "collecting allies" sub-game that many campaigns create IME. Rather than having 30 NPCs who could be going along on an adventure with the PCs, the PCs have a revolutionary front that the PCs can direct to deal with situations developing concurrently with whatever the PCs are dealing with.
- They can replace "followers" and consolidate them with "stronghold", into one easy to manage set of resources with a couple tables, a couple scores, and some named NPCs running different things.
- They give "downtime" resources the PCs can use to accomplish things that would otherwise take a bunch of in game time away from adventuring.
- Rather than spending 6 months crafting a legendary sword, you've recruited the famous smith and mage of the region to do most of the work for you on the ingredients, preparing the materials, smelting "impurities" into it and other impurities out of it until it has the metalurgical properties you need, etc, so that you can come in and take that bar of steel/gold/cobalt/residuum/dragonbone alloy into a blade, attaching the elemental ruby to the crossguard, and balancing that wild elemental power with runes of stasis and binding, and then affixing a diamond turned red by your own blood to the pommel, binding the power of the sword to your will.
- Rather than spending a bunch of time researching, you put the scholar and librarian you recruited when you saved them from their burning library during a demon attack to work on it, and just spend a day reviewing all the information they found for you, and then consulting your mage friend with that info to create a binding ritual to seal the demons back in the abyss.
I like mechanics to help create meaningful bonds between PCs and NPCs/nations/cultures/organizations, tying them more strongly to the world.
- When they save the Princess, and choose not to strongarm the Queen into a bigger reward than what is first offered, they gain an Ally, and Favors, which can be called upon later. When they make a big ask from an NPC, they gain a Debt that will be called in later. If they push those relationships too hard too often, they can lose them, or even have them turn against them. This should all be transparent to the PCs.
- When they say they're sending a message to the Queen to send a squadron of griffon knights to give them cover to get into the Necromancer's fortress without having to drain their resources on a bunch of small fights with minions, they know how big an ask that is, and how much stress it will put on the relationship, and can check that against the status of their relationship with the Queen.
- There are bonuses and penalties to different kinds of bonds or rivalries, which the players know about when they gain those bonds, and know what effect they will have on what kinds of situations, etc.
- Bonds and rivalries can help introduce a complication at an unexpected moment, give everyone at the table ammunition for improvisation and authorship of the fiction, if combined with simple mechanics that allow a player or the DM to react to a roll, a change in the action, etc, by calling upon anyone at the table's bonds, flaws, rivalties, ideals, debts, etc.