After I cleared out the first few quests, I finished up my main story quest, which left me with a message to wait for a level or two before the next quest. (Helpfully, major quest lines have an icon indicating that you can't get the quest yet as well as information about when the next one will be available.) I also finished my first Lancer quest and unlocked the Hunting Log, which is a new feature I instantly fell in love with.
Each class has a different hunting log, and each log has multiple tiers consisting of several targets. My Lancer's first few tiers included Marmots, Funguars, and Ladybugs. Upon killing a designated number of these enemies, you get some gil, some experience, and a mark toward completing a tier. Complete one tier and you unlock the next one.
Simple? Definitely. But it also gives you added incentives to go out and kill things as well as another objective to work toward. The log has other major benefits as well, but for combat-related classes, the impetus to go out and fight multiple targets really spoke to me.