The FATEs in low level zones like lower la noscea and central shroud can all be solo'd.

After level 12 or so, you should be going to Aleport. You do FATEs in Aleport (preferably with a FATE party... there's almost always people in the zone) until level 20.

At 20, you go to Quarrymill and get in a FATE party there. Quarrymill can take you all the way to 40 if you like, but most stop around 32 to go to Dragonhead. Level 39-40-ish you can go to Revenant's Toll (way better than Dragonhead). Once you hit 43-45, you go to Northern Thanalan (Cerulean Processing Plant). That will take you to 50.

Very much like FFXI and the "best" leveling areas.