What are the best fighting styles?

Utility. Utility. Utility.

"Just damage" is a bad sign.

Tier List

A tier list isn't a great way to value each of these fighting styles because the majority of them are situation and your mileage may vary (YMMV).

S Tier: Closer Quarters Shooter (UA), Archery A Tier: Blind Fighting, Defense B Tier: Interception, Protection, Superior Technique, Unarmed Fighting, Thrown Weapon Fighting, Dueling

Blind Fighting: Blind Fighting is favorite fighting style in the game. Fog Cloud, Darkness, etc. are great ways to get advantage on your attacks (and it's a great way to escape from opportunity attacks) -- this technique might be annoying for the rest of the party, but if your party is aware of the strategy, they'll adjust to it. It also protects you from the Blindness condition and ensures that at least someone in the party can deal with invisible enemies.

Defense: A +1 bonus is pretty boring but AC is bound in 5e and any increase to AC decreases the amount of damage you take by about 5% for each increase in AC.