Here is the build: http://skyrimcalculator.com/190437
Basically, I would conjure dual blades, or use two regular or enchanted blades, and summon atronachs for support. I would sneak a bit to get in a first shot with bow, but not rely on sneak too heavily. I might decide to swap enchanting for illusion - we'll see. How much magicka would you recommend I get for this?

Only enough as to conjure your most costly summon. What that is will of course depend on the 50% reduction of the Expert perk and the Conjuration skill. Without actually testing this or researching the costs, I would dare to guess somewhere around 250.

Does it really cost 250 magicka to summon a storm atronach?

It will be dependent on several factors. That was just a blind stab at a figure.

EDIT : I'm now more curious. Let me fire up the game and create a test character with the console and I will report back.

Depends if you plan on using Enchanting to give yourself 100% reduction in Restoration and Conjuration. If you did, you wouldn't need to put any points at all in magic reduction.

If you are looking to be more legit, persay, then here are base the numbers for summons (Assuming you have 15 points in Conjuration to begin with. They will reduce as you grow in skill). You can do the math to half them.

Novice:

- Sword: 82
- Familiar: 94

Apprentice:

- Battleaxe: 149
- Flame Atronach: 132

Adept:

- Bow: 183
- Frost Atronach: 189

Expert:

- Storm Atronach: 284
- Dremora Lord: 316

If you halved them and want to summon a monster and a sword in a fight, you could do with about 200-250 magicka.

EDIT: A master of Conjuration could summon a bow, then a sword and a Dremora lord with exactly 194 mana, so you would only need 200.

With a Conjuration skill level of 76, and having the Expert perk, the Conjure Storm Atronach costs 106 magicka.

That is without wearing any spell reduction gear.

Actually, the base cost for that spell (assuming zero Conjuration skill and no perks, enchanted gear, etc.) is 322 Magicka. At 100 Conjuration, the cost drops to 191 Magicka, again assuming no cost reduction gear or perks. It's an Expert level spell, so at 75 Conjuration, plus the Expert Conjuration perk (50% cost reduction) it costs 107 Magicka to cast.

I had it all calculated out and forgot to hit post. Sorry about the repeat.

EDIT : I actually went in game and checked. I don't trust my math skills anymore....not that I actually had any to start with.