Well, I would definitely, as you are doing, wear the hood at the moment. The rest you can keep heavy armor. Try to find a necklace and ring with magic enchantments. You will also have invest in magika more so. Although, since you won't have to worry about alteration, you will have a little more magika to work with.
If I was you, I'd focus on that enchanting. Start gathering as many soul gems as possible. Go mine some gold ore and silver ore and smith a ton of rings to enchant them, and watch that skill rise. You don't have to reach the top just yet, but get it decent to wear you can enchant all of your armor and jewerly with magic related enchantments. If you're going big on destruction, you have the potential to completely cut the cost of destruction magic to 0, so it will be unlimited. Same goes for all school of magic, and that way you can save perks. So you can do those kinds of enchantments, enchantments that increase magika and magika regen, etc. That's what I would do asasp, it worked very well for my character.
Also, as far as the armor weighing you down, try to increase it to get that perk in the heavy armor skill tree that will eliminate that problem. Just let a bunch of mudcrabs beat the plops out of you, and then heal yourself. Repeat. Does wonders for restoration as well.
Good luck!