Hypnos
L'Empereur
I wish I ruled over a KingdomWanderingJester said:In general, each great house rules over a kingdom of Westeros, hence 7 great houses for seven Kingdoms. Lannisters over Westerlands, Starks over the North, Tully over the Riverlands, Targaryen over the Crownlands, Baratheons over the Stormlands, Tyrells over the Reach and Martells over Dorne. Here's a reference fore them for more details.
Great houses
Now for Reach specifically, the head honchos are, as stated, the Tyrells (which you've observed). However there aren't much of a formal "rankings" in regards to who rules after them. Tracing back to the original rulers of the Reach, House Gardener, the most direct line and strongest blood would be House Florent. However possibly the richest of the Tyrell's bannermen includes House Hightower, who rules over Oldtown, the oldest town in existence in Westeros, as the name implies, the Tarlys, possibly the best Marcher Lords the Reach owns militarily speaking, and the Redwynes, who controls the largest fleet in existence on Westeroes. Not to be brushed off are the Rowans, which are similar to the Tarlys in that they have an impressive military force, but have more quantity to the Tarlys quality.
Also important to mention are the Houses of the Shield Islands, pretty much the only thing that's stopping viking/Ironborn raiders from pillaging along the entire Mander River (which spans most of middle and Northern Reach). At the moment in the RP, the de facto leader is Lord Grimm of House Grimm after the repelled assault by the Iron Fleet earlier IC.
Here's some book canon details if you want to read up a bit, though none of the recent events obviously relates to the RP's story.
Reach
Bonus: Here's a useful map I use for reference in regards to Planetos in general. If you're interested as well.
Interactive Game of Thrones Map with Spoilers Control
And that reminds me, I've been meaning to ask Tyrell for that high lordship, though I suppose this isn't th time considering they're at a funeral.