If you're stuck or wondering when you'll get something (like a chocobo), chances are the answer is: follow the main story.
There are several useful websites out there with relevant information.
A great database website:
http://xivdb.com/
A great website detailing jobs, strategy, the world map, dungeons, etc:
http://www.ffxivinfo.com/
You can probably find all the information you need about classes and jobs there.
You'll have to pick your first class which you will need to level to 10 before you can change to another class. To change to another class, you need to venture to the appropriate guild and do the class quest for that guild. After that, switching classes is as simple as switching what weapon you're using.
Once you hit level 30 with a class, you're able to choose a job: a more focused version of your class. For instance, a thaumaturge is able to select a black mage which boosts INT and gives you some job specific abilities that THM doesn't have. In exchange, you lose some of the cross class abilities that THM has access to. You also need to get a secondary class to level 15 for your job. It differs based on which job you choose. So, I'll give you a run down:
GLD (gladiator) changes to PLD (paladin) - tanky class; uses sword and board
MRD (marauder) changes to WAR (warrior) - tanky class that will receive buffs here soon; uses 2 handed axe
PGL (pugilist) changes to MNK (monk) - punch things with your fists! great physical DPS class
LNC (lancer) changes to DRG (dragoon) - stab things with your spear! great physical DPS class
CNJ (conjurer) changes to WHM (white mage) - one of the two healers; focuses on heavy AoE healing and is great for heavy healing on single targets
ARC (archer) changes to BRD (bard) - ranged physical DPS; bard uses songs to buff allies and does quite a lot of DPS by itself
THM changes to BLM - ranged magical DPS; focuses on heavy damage spells that require a little time to cast; great burst damage
ACN (arcanist) changes to:
SMN (summoner) - ranged magical DPS; uses a pet and focuses on DoTs; very high sustained DMG
SCH (scholar) - the second healer; uses a companion fairy to help heal which gives unique buffs; focuses on shields and AoE shielding
This is a gross simplification, by the way. :)
You also have the option to level up crafts and gathering professions. You do the same thing: go to the guild, accept the main quest, equip the weapon, and become that specific craft or gathering profession.
Cities that have the specific classes:
Limsa - ACN, MRD, culinarian, blacksmith, armorer, fishing
Ul'dah - PGL, THM, GLD, alchemy, gold smithing, weaving, mining
Gridania - LNC, ARC, CNJ, carpentery, leather working, botanist
Here is a website with the races:
http://www.final-fantasy-14.org/races
Edited, Dec 4th 2013 8:41am by HitomeOfBismarck