I think that Tolkien does say somewhere that the Riders were organised geographically -- Éomer I think in T2T, when talking to Aragorn, says that he is responsible for the East-Mark.  It makes more sense for the Riders to be organised in this way (i.e. with provincial centres at which warriors gathered) than to have them all gather at one central point (it would take too long to get there).  Also, warriors from one area would all know each other and be more comfortable fighting alongside of each other.  A certain bond of trust and reliance would already have existed -- as opposed to fighting side-by-side with total strangers. 
     Presumably, only the King did have the authority to call up all the levies.  A marshall such as Éomer could call up the levy of the East-Mark, but clearly had no authority in anyone else's mark.  I'm not sure if this resembles any modern military system, but take the system of the Persian Empire.  Each satrap commanded his satrapal army and was responsible for the defence of his satrapy from outside threats and for the maintenance of good order within it.  But only the Great King could order all satraps to raise armies for a military undertaking of the whole empire. 
     As to whose plan I prefer: I think Elfhelm was right to want to abandon the fords and move farther East.  The real threat was not directed at penetrating Rohan from west of the fords, but rather coming farther north from Isengard and directed ultimately at Edoras.

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All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.