Choosing a class in FFXIV can be a hassle if you have no prior experience in similar games. Reading about the classes in the official website certainly doesn't help very much, as the site doesn't give much specific information on each class's strengths & weaknesses.
Here, I have summarized all the existing classes of the game based on some forum members' knowledge as well as my own experience. I hope this will give a better overview to new players to help them pick their favorite class(es) in the game that suits them.
Remember you don't have to limit yourself to just 1 class. You can pick everything with a single character if you want. In fact, picking more classes are usually beneficial as you will be able to use more "cross class skills".
In a party of different classes, the role of a Tank is to absorb damage for the team. The Tank class is responsible for using specific skills to attract enemies so that the rest of the party remains safe. This is based on the building up of "Enmity" (a.k.a. "Aggro" or "Hate"). When an enemy is being attacked by a DPS class in your team, enmity will be generated towards the DPS, resulting in the enemy attacking back to that DPS. Similarly, Healers generate aggro to all nearby enemies by healing your party members. A Tank's job is to maintain the highest enmity on all enemies in the area, so that none of them would attack DPS's or Healers. The Tank class cannot do as much damage to an enemy as a DPS, but it has skills that can create enmity to outmatch the enmity of other classes. Since Tanks always take the lead to walk into enemies first, most of the time it is assumed a party leader role.
The Healer class, as easy as it's name suggests, is responsible for healing any injured member in a party. It is also responsible for creating barriers to protect everyone. It is not very strong in dealing damage comparing to DPS, but healers can still do some attacks.
The DPS class (Damage Per Second) is a class that is responsible for dealing damage to enemies. All DPS classes are somewhat "squishy", and are susceptible to injuries. Thus, a good DPS must know how to dodge attacks properly, and perform its "rotation" of multiple skills in maximizing damage to the enemies.
Job Specificity at Level 30
When you take up your job at level 30 by equipping the job's "Soul Crystal", all your stats will be greatly increased. Your main attribute will increase by 20 points, and all other attributes will increase by 10 points. You will also have access to "job-specific skills". However, your cross class skill slots will be reduced from 10 to 5, and you will lose access to cross class skills of many classes, leaving you only a few choices to pick from. This design is to ensure a person of the assigned role in a party would actually fulfill that role. This is to prevent a party being formed on the Duty Finder where people fail to do what they are supposed to do. If you try to unequip your Soul Crystal to keep all those cross class skills, yes, you will have more utilities, but you won't be able to use them effectively, and you will likely fail in delivering your job's role due to the lack of job-specific skills and the deficit in stats.