My experience with a battlemage is that you must be careful abount not turning him into a melee tank. Melee is easier to use than magic and you typically will run out of magicka often.
So you might need to make some choices to favor magicka before you start the game. Maybe use a Breton to get his extra magicka pool (altmer is probably too fragile for a battlemage) and one of the magicka-improving birthsigns instead of the obvious 'The lady'.
Among skills, you should include alteration and mysticism, since those are the two swish army knives among skills, which do all the small things you need like fast travel, levitation, unlocking, soultrapping, everything related to water and telekinesis plus absorb spells (absorb health is really nice) and shield spells.
Block would probably not be very useful as a minor, so either make it a major and use shields or drop the skill.
With reagards to speechcraft, you can choose that or illusion. Speechcraft is easy to use and don't require magicka, but it has only few uses compared to illusion.
I like to have armorer as a skill to repair my own armor and maybe conjuration (which should be a major if included).