What Urthdigger said, you can continue your storyline on any class and whatever class you do them on will get the XP.

The nice thing is that the level 15-ish quests will bring you to the first of the instanced dungeons and those are very nice XP that are available to any of your classes that are the minimum level (which is easy to do through the early class quests and hunting logs). On top of that, if you have any combat class that is higher level than your current one, you get a 50% XP boost to many forms of XP so don't feel like your alternate classes are dead in the water or anything.

Something of note is that you should unlock the challenge log from a level 15 quest in Limsa Lominsa's adventurer guild. There are tons of objectives in it that all give some great amounts of XP and money, plus it resets every week.