Okay, I've been lurking in the 'SanSan' fandom spaces for years, on Tumblr, AO3, the works. The ship dynamic itself is the anchor—the gruff, scarred knight and the naive lady—so most popular fics lean into exploring that from every angle. But the 'ships' within the ship? The specific alternate universes or tropes that get the most traction?
Post-canon fix-its where they end up together after the show's mess are huge. Fics where Sandor finds Sansa again in the Vale or up North, and they build something quiet and domestic away from the political garbage. That's the bread and butter. The other massive category is modern AUs, which honestly surprised me at first but now I get it. Coffee shop AUs, college professor/student dynamics (with all the careful handling of that power imbalance, obviously), or even rival business owners. It lets writers play with the core tension—his roughness versus her refinement—without the Westeros baggage.
Less discussed but still a big niche is the 'Clegane's Keep' scenario. Fics where he actually does take her with him when he flees King's Landing, and they have to navigate that isolated, gothic castle together. It's pure forced proximity and character study fuel. I sometimes prefer those to the more polished reunion fics; there's a rawness to them that fits the characters better. Also, crossover fics with 'Jane Eyre' or 'Beauty and the Beast' are their own little micro-genre, for obvious reasons.
Honestly, the popularity often cycles with fanart trends or if a big-name writer drops a new series. Right now, I'm seeing a lot of 'older, wiser Sansa returns to King's Landing as queen and encounters a legitimized Sandor' plots. It's all about giving them a semblance of the peace the show never did.