Protip: Fire against Frost, Frost against Thunder and Thunder against fire.Use Fire against All types of Undead and especially Draugr.
If the Dragon breathes Fire, use Thunder, if it breathes Frost, use fire, you know where this is going.
It actually works, and pretty well.
/edit: Also, against bandits and such, use Fireballs if you have no Companions.They do AoE damage, are cheap in mana and do good damage.Overall, Fire is the best type of destruction magic because all the Firespells are relatively cheap with good damage + Fire is the best against Draugr which you fight very often.