A starting character has the base stats stated on their class page and access to all the Rank 1 abilities of their class. As they advance their power grows, both in terms of stats and abilities. Starting at the second level and every second level thereafter a character gains +10HP, +10 STA, +10MP and +1 Initiative. At level 11, their abilities grow accordingly and they gain access to all Rank 2 abilities for their class. At level 21 finally, they gain access to Rank 3 abilities.

For an easy reference check the which can instantly calculate your stats and show the abilities you have access to appropriate to your class and level.

Note that if you have a 0 for any stat it means you cannot increase it by levelling or any other means. For example, if you start with 0 MP you will never be able to gain any additional magic points.