Level up one class or several from the beginning.

[Shougun]

Once you reach level 30 on a class you will get the opportunity to unlock a job, which will add significant power to your class - that is one bonus for leveling a particular class up. You will need to level one side classes up to half of that in order to unlock the job (consider leveling two for cross class abilities).

Certainly play whichever fits your fancy if it means having fun; however, in terms of efficiency keep in mind of the Armoury bonus which works by granting you extra EXP when you level jobs lower than your highest leveled job - which is 100% until 50. That can mean a lot for the lower leveled jobs and classes. To be specific 100% exp bonus for jobs under your highest leveled job till level 50, and 50% for jobs under your highest leveled job past level 50.

Also you will have once a day special bonus for running each Roulette found in the Duty Finder, they're all pretty good but the low level roulette has been known for its great exp bonus. Guild Hests also have a unique one time bonus exp for each DoW/DoM class(/job) that exists outside the bonus of the day from the Guild Hest Roulette. Talking about bonuses, the Job (type) in need bonus is each time- so if it says it needs a tank and you get 5K gil you can continue to rerun that content for that bonus till you're not the job in need ;P (tanks and healers are almost always in need).

So for efficient use of time, I recommend running at least the low level roulette once a day bonus to level, and to level one job you like up to 50 following the Main Story line. The main story has added rewards to help gear you to heavensward content since heavensward was added, you shouldn't be spending much gil on gear so long as you pick up dungeon gear and quests that pass by with nice rewards. Also, you can scan leves for gear rewards if you really needed something to wear as they sometimes have equipment as a reward. I do not recommend leves for battle classes past level 15 (unless you see something you want). Leves as well as Ixali beast tribe quests and Grand Company Turn Ins are excellent leveling opportunities for crafters and gatherers however.

This link has some info on exp too: http://ffxiv.consolegameswiki.com/wiki/Experience

See challange log and hunt log for even more EXP opportunities, some of which will happen with very little modifications to the way you are already playing but will reward great bonuses.

Edited for armoury bonus clarification.