Chocobos only, please.
I don't want to end up seeing some random motorcycle or car obtusely bursting into my traditional Final Fantasy world, ala WoW. Also...seeing someone randomly striding across the dunes on something like a Peiste or an Eft or Goat just seems like it would be a bit goofy to me. I couldn't take that seriously to any degree. Chocobos have always been a mainstay of Final Fantasy - they should stay so in XIV.
I do think however, that the chocobos should obviously be earned.
A status symbol, of sorts. I remember the feeling I'd get from riding my Green Chocobo that I raised to a party location in XI. I was proud of it and the work I invested into raising it, and it felt neat having something unique and special that was specific to me and what I wanted it to be. And then to get a chocobo lisence period was a rite of passage in XI.
And once we have the chocobo system ready, commence with the breeding, armoring, special stats, racing, etc, and XIV could have an awesome "mount" system.
The more customizable you can get your bird, the better.
As long as it's all earned and gives people something to focus on and work towards, I'm happy.
As far as what they can do and what purpose they would serve:
I liked how chocobos worked in XIII, actually.
There were certain zones you could only get to via chocobo. This gives people a reason to rent them aside from the obvious things such as mob-free travel and speed.
We should be able to rent a basic ("yellow") one from the stables whenever, for a somewhat reasonable price (not the chump change in XI...only a few hundred gil for a chocobo seems insulting to them) or summon one we've earned/raised whilst in the field. This could be an item (such as Ghysahl Greens) a piece of equipment (added in a new slot, not worn around the neck...shame on you, chocobo whistle, taking up my neck slot with your horrid cool down time.) or an option on the main menu.
No birds in town. They "stay at the gates" (sort of like calling a retainer, you could have a chocobo valet at the entrance to each city) or if they're a rental, they're returned to the agency. This would allow you to have multiple chocobos, the same way we have retainers. (I.E. Blue Chocobo can cross deep rivers, allowing you to reach a certain zone. Red can climb steep surfaces. You have both for doing either thing. There can be 'black' chocobos that can reach any area, but obviously those need to be prime rarities. I also understand someone might just want a black chocobo for appearance sake, so color shouldn't nessecarily the only indicator of ability...just as an example. Maybe 'classes' for the chocobos?)
What would be neat would be to have saddles or heraldry for your chocobo specific to your LS or other group (player run companies comes to mind, if that's still happening). Armor and saddles could all provide the chocobo with boosts to certain respects, such as how long it can sprint, how many times it can get "spooked" (avoid aggro before some adverse condition takes place) how well they can dig or find treasure, etc.
Plus, all of this could be a big gil sink to help de-bloat the ecomony, and could maybe even add a new class - A chocobo breeder class! ^^