-Confirmed quests-
Story Quests - About 15 quests which you do 1 after the other which tell the story of the character.
These Quests are always interesting, but too many of them can become monatonus.
-Unconfirmed quests-
Loot Quests - You go around fighting monsters to find their loot to complete the quest. Most likely they'll be one after the other. Your rewarded with Exp and Gold
It depends on how difficult you make getting the items the difficulty should be worth the reward.
Protection Quests - You escort someone from one place to another. This would reward you with Gold, Exp and maybe even an unlockable or an item...
These are something that belongs in Final Fantasy series like Crisis Core, but they can work especially if in your world you create a community of monster hunters or something like that.
Profession Quests - A chain of quests for that profession. They could be anything. It's worth Gold, Items and at the end that Profession's final skill.
These quest only make sense if you are going to have a profession you need to have training or "quest" in order to prove that profession.
Expert Quests - Quests that can only be accessed after you complete the Story Quests. They could give you anything. But be warned, they're to be very hard.
These could be fun and challenging, but maybe offering an item if you complete them all would give them more interest.
(If I have missed any type of quest, please tell me)
I didn't see any trading quest which are a standard in most RPGs, but not needed if you do not want them. These kind of quest can link other kinds of quest together. For example, say the old man has something you want, but in order for you to get it he needs something the old woman has, but she needs you to kill a monster first.