タルタリヤ

Polar Star
Best overall for a main DPS build as the effect is easy to keep up with Childe on the field.

Aqua Simulacra
Best overall for a burst DPS build as you don't need to fulfill any conditions to keep the effect active

Thundering Pulse, Skyward Harp
These weapons are comparable to Polar Star and Aqua to the point that using any of them is valid instead of pulling for 1 specifically.

Viridescent Hunt
Best 4 star option and easy to get with battle pass. Effect helps grouping and the main stat helps your Crit Rate needs.

Blackcliff, Mouun's Moon, Prototype Crescent, Rust, Stringless
Alternative F2P options depending on what you have available. Dmg is comparable between these.

<sands> ATK%
<goblet> Hydro DMG Bonus
<circlet> CRIT Rate / CRIT DMG

CRIT Rate
CRIT DMG
ATK%
EM
ER (to an extent)

1) Elemental Skill: Foul Legacy - Raging Tide
2) Elemental Burst: Havoc - Obliteration
3) Normal Attack: Cutting Torrent

Childe's Talents:
Burst and Skill contribute roughly the same amount of damage in the main DPS rotation, so both should be levelled equally. If built as a Burst DPS then obviously Burst should be the primary talent. If you plan to use Childe on-field during his downtime you will also want to level his Normals to help his Charged Shot dmg.

Childe's Artifacts:
You can use 4 piece Heart of Depth, 2 piece HoD with Atk% or Noblesse, or 4 piece Shimenawa's as they are roughly the same dmg output although Shimenawa will have a higher ER requirement to comfortably cycle. Nymph's dream is roughly a 5% increase from 4 piece HoD, wouldn't recommend farming if any of the previous options are available.

Polar Star

Aqua Simulacra, Thundering Pulse, Skyward Harp, Viridescent Hunt, Prototype Crescent

<sands> ATK%
<goblet> Hydro DMG Bonus
<circlet> CRIT Rate / CRIT DMG

CRIT Rate
CRIT DMG
ATK%
ER

1) Elemental Skill: Foul Legacy - Raging Tide
2) Elemental Burst: Havoc - Obliteration
3) Normal Attack: Cutting Torrent

Childe isn't assumed to vape his burst for this weapon and artifact ranking, making 2 NO worse, EM from 2WT becomes less useful stat for both teams.
Freeze Childe:
4BS will be better than all sets mentioned above, and CR Weapons such as VH, Harp will be worse because it's hard to not overcap crit with it, but Polar star remains BiS along with Thundering pulse assuming no use of Bennett, or TTDS.