To start off with, I'll list the assumptions I'm making (which are based on what scant info has been released). See here for the details.
a) Grand Companies will be NPC entities, not player-run
b) Grand Companies will supply quests of 'epic' nature
c) Grand Companies will also offer soloable quests
d) Grand Companies will have interactions of some sort with linkshells
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Now, for my dream / vision / suggestion
Grand Companies off a wide variety of quests
Quests may range from defending a hamlet from on oncoming horde of beastmen, to attacking a Garlean Attack Force, all the way down to gathering materials needed to create Grand Company buildings
Direct Rewards for are Grand Company Marks
Gil will matter very little with regard to Grand Companies. Instead, characters prove their worth by completing quests for the Grand Company, and receive Marks to represent how much 'favor' is owed the character. Unlike other Marks in the game, I think that GC Marks will be trade-able, and hence can be bought/sold for gil.
Grand Company Marks are Used to Access "Guild" Features
If enough GC Marks are pooled to the leader of a linkshell, that linkshell can then purchase / rent facilities from the Grand Company that mirror features usually granted to guilds in other MMOs. This list could include:
a) Linkshell bank
b) Linkshell emblem on cloaks/shields that can be worn by linkshell members
c) Linkshell common hall
d) Linkshell merchants in hamlets
e) Linkshell sailing ships or airships
f) etc <help me fill this in!>
Grand Company Marks can be used by individuals
Solo players may complete quests and accumulate GC Marks, and so to not leave them out, certain things may be made available to individuals, including:
a) Purchase / rental of chocobo mount
b) Purchase of a house
c) Company-specific gear with a unique look
d) etc <help me fill this in!>
These are all some random, wishful thinking-type thoughts, so please feel free to chime in with suggestions or more ideas!