Depends on the build, but as this is a game about fighting Dragons, most of them have some way to go about it, or avoid the Main quest entirely.
Which type of character works best? Archer, hands down. Stack up some magic Resistance, and stay back from the physical attacks, puncushion with impunity.
The worst is probably the pure Melee'er. The Dragon doesn't have to land until you have Dragonrend, so prior to that, you spend a lot of time running around slowly in your armor with your weapons in hand, and waiting for a chance to counter-attack. I don't generally play these types. Even when I do, I get a good bow, and invest in some Archery because Here There be Dragons.
My favorite? Magic. Gain, stack up those resistances, but the Mirmulnir combo is Lesser Ward, and Lightning Bolt. Even that puny little Novice Restoration spell blocks dragon breath like nobody's business, but it drains a lot of Magicka, and takes a little while to charge up, so you really have to time it when he says "Yol,.." Once you get Ward Absorb, you don't need to upgrade it further, just use it to charge up your blue bar for some Thunderbolts. The nice thing is you can cast right through it, so you don't have to let it down until it pauses to take a breath.
The ultimate are my World Eater Cherry Tapper builds, which were designed for one thing, Alduin's Bane. I started a little contest on another forum to beat Him at the Throat of the World in as little time as possible at the lowest level with little to no equipment other than the Scroll, on Master.
And the winner is... Breton, Atronach Stone, double cast (Not Dual Cast, in both hands) Walls of Frost. Dragonrend, followed by Shin as soon as He THWOMPs down, hose his footprint with multiple instances of DoT that drains His Stamina so He can't take back off. Wearing nothing but a loincloth, He didn't last as long as the daily power, and was powerless to hurt me with 100% Spell Absorbtion.