You've missed out on (IMO) the most enjoyable play style. I consider it (or anything of the type like Spellsword) magic in one hand and one handed weapon in the other, considering Skyrim's duel wielding system. You'll have easy access to both while in battle, slashing at enemies at one point and then throwing fireballs or summoning a Daedra a second later. As for magic, Destruction and Conjuration are likely your best bet, what I've used with my character. Perhaps with an addition of Restoration as well, for some quick and effective healing.
The most solid things I've notice with Battlemages...
Heavy Armor.
Axe (1H only) or Blades (1H or 2H).
Destruction Magic. (Master)
Conjuration Magic. (Expert)
Restoration Magic. (Adept)
Alteration Magic. (Adept)
Enchanting.
~Spells list~
-Destruction-
A whole set. (Fire, Frost, or Storm).
-Conjuration-
Resurrection spells.
Daedra summoning.
Bound Sword.
-Restoration-
Any Healing Magic (Adept or below).
Wards.
-Alteration-
Shield Magic.