There's really only a handful of quests you should do to level, the rest are story fluff etc.
1: The Starting quest from Arua's Fairy in Adventure Plains. This just gives you some boosters and a Choropy Mount for free [limited time]
2: Doonga + Krawfy Kill Quest [40+ and 50+ I believe] You get it from ... Bith? There's an NPC with a question mark on the docks, can't miss him.
3: Lunaris Bears Kill Quest from Coffington in Mana Snowfield [Think it's mana snowfields, someone will correct me if it's wrong, don't worry] Go there as soon as you get 70+ and can travel to Luna. Lotta party's there.
Finally, if you find yourself stuck solo after getting to Orlo, there's another explorer/coffington quest in Fossil Sanctuary which offers 4 kill quests. They come in handy if you're on your own. But by the time you get to 210+ you can just level in Dungeons.
There's a handful of useful quests, but hardly any are designed to level effectively with. The quest system is in need of some TLC but since Qilin our old quest writer left, no one has shown any love for the questers in ROSE.