There are a few low level sidequests in each area that you should be able to take regardless of where you started, but yes, a lot of others are only unlocked in conjunction with the Main Scenario quests in that area (which, for levels 1-15, you'll only get if you started in that area). Since after level 15, the Main Scenario quests are merged into a single storyline, it also means that from that point on, you'll be unlocking all the sidequests as well. It's just the first 15 levels worth that you won't unlock everything, if you're not doing that region's MSQ.

You won't be able to level or gear more than one or maybe two classes with questing, though. Beyond that, you'll need to find other sources for both XP and gear. As Enkidoh mentioned, there are enough XP boosts available that the actual leveling isn't as hard as that sounds. As far as the gear provided by quests, it's the same as is offered by NPC vendors and the same as Normal Quality results from crafting, so you can find equivalents from either vendors or the Market Board.