I'd expect company to work in a similar way of FFTA guilds.

A guild will have the overall rank and a rank on several attributes. As you complete company quests you will raise the company ranks, which unlocks higher (and harder) content.

Being able to have our own ship will be awesome, specially if, instead of spending tremendous amounts of gil, they make it like "you can have it IF you can build one" They giving a monstruous list of materials and, once you get them all (including some exclusive stuff...i'd hate to see people, instead of buying a ship just buying all parts...would be a shame since would have no merit in this) you receive your ship.

Same working for the building...like being able to have several features there, like the already said bank, build guild facilities for members only (a guild in Ul'dah with Woodworking guild facility would be awesome), customize the place, add a wanted board for members and even allowing expansion of guild size based on its rank.

In an extreme way, allowing companies to offer their own leves at guildleve corner (obviously in a separated NPC) when they, as example, don't have the needed crafter, would be awesome too!

But still, need more info before we can do more than just toss random guesses.