Basid
Battle mages are nukers. They finish large groups monsters, they dont have much single target skills.
Skills
Skills wich should keep up
-Mana shield absord 30% dmg taken to your mana. That is important, because you have much more mana than hp.
You should upgrade that level 1-3. If you think you hide behind other party menbers and you dont take damage, dont train that skill then. For me that was usefull :D.
-Focus, upgrade that lvl 5. That's amazing skill think it lvl 5, 24% more magical power and 20 intelligent. That means like 25% more powerfull attacks.
Damage skills
Almost all Battle mage skills are usefull.
I recommend that you max skill Fire emblem and Energy Condensation.
Magic missile is usefull too, but if you train it, it should be level 3 or more.
Tornado level 2 for Blizzard storm. Tornado isnt so good skill, only use if monster getting too close you, flip and kill them to the ground.
Blizzard storm, AMAZING, max that, That skill shares first place with Fire emblem.