im also new to this game but from what i understand about the arc mage is this
you need to get these skills...
Active:
Fireball (MAX THIS)
Call Lightning (MAX THIS)
Cold Wave (MAX THIS)
Missle Storm (useful skill, does decent damage, low cooldown)
Foresight (MAX THIS)
Summon Golem (MAX THIS, GOOD FOR BOSS FIGHTS)
Passive:
Magic Arrow (so far i only have 1 skill point in this because the damage only goes up by 1% after the first skill point, YOU MUST PUT AT LEAST 1 SKILL POINT HERE)
Golem Master (not lvl 30 yet but this seems like it will be useful)
Chaos Mana (again not lvl 30 yet but double casting in Com2us's other games it AWESOME)
Also i personally find that mages do more damage when they have a wand and shield equipped instead of a two handed staff, more Damage Per Second (DPS) which means more total damage also it gives you more defense (the shield)
NOTE:
Mages can only use one type of shield (Light Shield)
I hope this helps
Lucio lvl 23 Arc Mage