As Kevin Y said, you need to unlock then beat mission 14 to unlock the chocobos, which requires you to beat 13...this is the chain:
1->2->3->5 and 7->12->13->14. The link has all the location maps for the Bosses+Cieth Stones.
After you beat 14 you will find Chocobos scattered throughout the Archelytte steppes. Hope this helps.
Final Fantasy XIII is (by concept) to a large degree a strictly linear game. Most of the time (with the exceptions given below), the levels are a simple "tunnel" with no forks. You will only be able to stray off the path for some meters to find hidden treasure spheres or optional enemies. There are no side-quests in the traditional sense and you will only follow your main objective. Once you leave a level, you will not be able to return to the previous visited stages. This is a large departure from the gameplay of earlier parts of the series (say, FFVII).
On the plus side, the graphical representation and the atmosphere/mood of these tunnel levels is awesome. In fact, if you switch off the minimap you may even forget the limited topolgy and enjoy the surroundings. Also, the game uses the restricted degree of freedom for its intense and fast paced storytelling.
The exception from this rule come only very late in the game. FFXIII consists of 13 chapters. Once you reach Chapter 11, you will have access to a number of non-tunnel levels where you may roam freely, that is, as far as you can beat the enemies that stand in your way. Also, a number of simple hunting missions becomes available, where the simplicity refers to the structure of the quests and by no means to the challenge of the enemies. In fact, at this stage you are not expected by the game to be able to complete all challenges of Chapter 11. Rather, you should complete some easy hunting missions and move on with the storyline to level up. That is, you leave Chapter 11 to beat another sequence of tunnel levels in Chapter 12 and the final boss fight in Chapter 13.
However, from Chapter 13 (and even after finishing the final boss), you will be able to travel back to Chapter 11 as often as desired to beat as many optional quests as you like. This is intended as some kind of open-ended-like gameplay where you can find the characters ultimate weapons and fight some really impressive special enemies.
Personally, I really enjoyed the game yet I would have like a more open world. The story was exciting and was presented like an intense and fast-paced action movie. Yet, it doesn't reach the quality of earlier great storylines (like VII, VIII, or X). However, the real strength of the game lies in the combat system, which is strange at first, but works out great once you get used to it. I recommend to give this game a chance.
Best Answer
They are self contained.
In fact, it's not even true* that all final fantasy games take place even in the same universe - they are normally connected by having similar story lines and morals. There tends to be guest appearances and other bits that carry on between games such as item names but nothing that would reduce your experience of the games without prior knowledge.
Lightning returns is even a distance relative of the other two, that being while the same characters appear in in L-R you don't need to have played the first two to follow the story. It's 1000 years in the future after all!.
If you were to start with XIII-2 - it does have a 'What happened in XIII' bit where you can remind yourself/learn what happened prior to the beginning of the game, explaining enough that you can just start at this point.
*Some fans have 'proven' they are all in the same universe, but there's nothing cannon to prove it.