Why does every body jump on poor Dragon Arrows? As Eldritch mentioned and I'll emphasise, apart from removing range penalies, Dragon Arrows are armour piercing! They will make almost no difference against mobs like peasants but are lethal against the high def units that dominate the later game. Even bosses, the turtle, laughs your spells off, try dragon arrows on your lonely archers and see the difference
Yeah as a mage it almost feels too easy fireball, fire arrow and later firestorm just one piece of advice for you, demons and that's all demons and all dragons (and you will be facing many) have at least 50% fire resistance, their top units have 80%! Though spells like Ice Snake do make up for this a lot of demon fights will be more CC/Buff than DD fights. You will be crying for support spells like dragon arrows!
Also second that advice mages do cast magic differently to Paladins and Warrior, the second two are more about buff and support with the Paladin maybe touching on some crowd control.
Fireball to second level is good advice for new mages, some like to rush to level 3, I prefer the long haul to Higher Magic 1 for the versatility - you'd be amazed how effective a beserk on Royal Snakes can be.