I picked Archery, because it's my second choice. My first is Lightning, and Absorbing his breath to power it. Either Ward Absorb, or Breton/Atronach Stone. My all time favorite was using the latter, DragonRend, and Wall of Frost to hose down His footprint so He couldn't take back off. I know Destruction was one of the choices, but by itself, the Magicka Drain means taking breaks to recharge. Without Absorption, it just takes too long. Alduin took less than a minute on Master difficulty with Breton/Atronach/Ice Lake.
A good powerful (Usually Mystic) Bow is quick, simple, and never runs out of Magicka (nor Arrows. It may time out, but by then, my magicka recovers, so I can just recast.) It's a close second, if only it hit-scanned like Lightning. The Staff of Jyrik Gauldurson, and Spellbreaker is another nice combo. Just don't get close, and they can't hurt you. I've also used Lesser Ward, and the Staff of Magnus (The casting cost means less if you're absorbing magicka with both hands) but the damage isn't as high, so it takes longer.
A Storm Atronach would be nice too, but it won't work reliably with 50% Absorbtion (Cast, and Recast before hitting the Power button while it finds a place to land.) Even Staves, and Scrolls get randomly soaked up, but if you're not using this cheat, the Archmage's Quarters has a Staff of the Storm Atronach that sure helps, and also adds some Enchanting Experience.
I would intend to use either a daedric or ebony bow with two enchantments at the same time on it.
adds for alot of double the amount of damage.depends on what type of dragon it is,it will come down in just a few hits depends on your perk.
The Nightingale Bow has Frost, and Shock at Daedric Tier (If you wait to let it level.) If you DIY, Absorb Health, and Shock would be a great combo, because the former heals you from taking Breath (not to mention falling rocks, on fire) and no Dragon is resistant to the latter. It'd also be handy for most other enemies.
There's so many ways to skin a dragon.