The best covenant for Fire Mage is Night Fae for both Mythic+ and Raid.
The other ability, Soulshape, provides more mobility to an already extremely mobile class.
When the full tree is unlocked go for Niya or Korayn for the damage increase.
At the start, Dreamweaver will provide you with two potency conduits early on.
Soulbinds and Conduits
Use any of the 3.
Disciplinary Command - This one is a strong option for single target but falls off in AoE situations.
Fevered Incantation - Increases your crit damage, this is going to be the go-to legendary for fire mage in the raid.
Firestorm - It's close to Fevered Incantation on ST and AoE and offers a rapid-fire playstyle. This is the best legendary for Mythic+ as it allows you to spam Flamestrike with Flame patch. While also being strong for the raid.
I would recommend this legendary for someone that wants to do both Mythic+ and raiding.
However, this legendary requires the Mage to be Night Fae and a Bloodlust effect to be used on pull to get the most out of it.
As for the second trinket you can use Unbound Changeling or Insignia. Honestly, it’s whichever trinket sims the best for your character.