My suggestions are as follows:

1) Get your room at the Inn:
Sleeping at the Inn will grant you a bonus to XP earned. This will help you a fair bit during your levelling. Also this quest can be done easily at low levels as there is no combat involved, nor do you even have to leave the city.

2) Progress through the Main Story line until you get to the Grand Company stage.
The main story line is interesting, fun, and gives you a LOT of XP which will help you level.

3) Progress through the Grand Company quests as you can:
They allow you to buy a Chocobo.
They unlock Ifrit, Moogle, and Garuda Battles.
The quests themselves are interesting and fun!

4) When you reach a stage in the quests that you can not progress further in you level, choose one class/job as your main and start levelling that. This will allow you enjoy more content.

5) When you reach the point you can start switching to a Job, do the AF quests.

If all goes well, when you reach level 50 you will have:
Full AF for that Job.
Baby Ifrit, Baby Garuda completed.
High rank in the GC (Maybe not lieutenant, but Sergeant).
Finished main story line.

You are now at a very good point to work on secondary jobs, or DoL/DoH or focus on end game content. Although many would suggest a DoL/DoH to help fill up your coffers.

Side Note: Levelling 0-30 with levequests is fast and should get you about 500-600k in Gil which is good ^.^