I've posted this here before, but again: I don't know nuts about the Free Worlds League. So I've a question: What would you consider the iconic Free Worlds League regiments? "Iconic" doesn't have to be mean elite; I think the Ghost Regiments can be considered iconic to the DCMS, for example.
The Free Worlds Guards and Marik Militia. Both are Federal brigades and so represent the entire League instead of just a single province, and they are the only brigades that wear the faction color (being purple, of course) as part of their livery. If I had to pull out individual units, I'd say the 1st Guards and the 10th Militia. The 1st Guards have been "the elite" unit of the FWLM for their entire history (except for that brief decade where the Knights of the Inner Sphere existed, and even then I'd still say the two were even in ability if not prestige). The Knights might have gone to Huntress, but the 1st Guards fought in the Great Refusal. The 10th Militia -- my personal favorite unit, so bias might be peeking through here -- is one of the rare few Marik Militia units that is
not just a cadre formation for the rest of the FWLM. They're a heavy-weight regiment, veteran-rated, and tough as nails as proved on Callison, Xanthe III, and Andurien. They're also one of only two Marik Militia units to remain solvent into the Dark Age era, having become the 1st Marik Protectors, a quasi-mercenary command devoted to the protection of former and unaligned Free Worlds.
Edit: Actually, I suppose the 6th Marik Militia is probably a better representative. As an assault-weight regiment, they're much heavier than the average FWLM unit, but they're famed across the League and beyond as shock troops
par excellence. They survived two or three scraps with the Dragoons during Anton's Rebellion and performed a picture-perfect orbital insertion on Arcadia that crushed an LAAF unit and saved Kristen's Krushers at the start of the Fed Com Civil War.