Night Fae is probably the go to covenant for raid and solo play. It provides significant burst and single target DPS. It is also really good for situations where you need to burst something down in short amount of time. However, one side effects with convoke the spirits is that you hit random targets within range of yourself.
The Night Fae covenant ability (Convoke the Spirits) casts 16 spells within a 4 second channel that you can cast while moving. 10 of these are damage spells and 6 heals (if ranged), on average. If you are in melee the 6 healing spells will most of the time be Rake and Thrash instead. So slightly more damage, but not enough to bother only using it in melee.
For Mythic+ I would recommend Kyrian as the covenant of choice due to the short cooldown and the high mastery gain every minute.
Kyrian is a pretty strong covenant for Balance Druid thanks to Pelagos (soulbind) being very strong. You can use the Kindred Spirits ability to link to yourself, which is safe, and gives you a flat 15% damage increase for 10 seconds.
However, It is better to use it on another DPS, that has good damage once every minute, so it can give them and you more damage. 20% of your damage is going into a pool that lasts for 20 seconds from the start of the bonding. Both you and your partner need to use up this pool over the duration of the bonding buff. Take care though, if either of you take damage, some of the the kindred spirits pool will go into absorption instead of damage. And if they are dead on the floor you will have a hard time using the ability or gaining anything from the buff.
This buff is quite hard to understand overall, so don't worry to begin with. Just link to a high dps player with either high damage at all times or with 1 minute cooldowns like MM Hunter, Fire Mage or Unholy DK.
Soulbinds and Conduits
Night Fae: Niya
The Night Fae Soulbind for the best damage output is Niya.
The Kyrian Soulbind for the best damage output is Pelagos.
For an AoE conduit, Stellar Inspiration is really good.
Balance of All Things
Balance of All things is by far the best legendary for single target at the moment. It provides burst moments every eclipse so it can be used well in various situations. It is also the best when it comes to two targets. In dungeons I would go BOAT (Balance of All Things) even though Primordial Arcanic Pulsar and Circle of Life and Death aren't bad choices.
Primordial Arcanic Pulsar
Primordial Arcanic Pulsar is a good legendary, but can be difficult in some scenarios due to the ramp for a Celestial Alignment proc which comes after you have spent 300 AP. Though it can be BiS for some high keys, at least with the fortified affix.
Circle of Life and Death
Circle of Life and Death is a good pick for dungeons, but can be a hassle to play with.
These trinkets are a blast for Single Target damage and priority target burst. The impact is that you need to plan ahead when you go for these two trinkets due to the 20 second cooldown when you have double use trinkets. So you use Empyreal Ordnance 20 seconds before your burst and then use Inscrutable Quantom Device with Celestial Alignment + Convoke the Spirits.