TLDR - Place unenchanted weapon/armor + x * void salts + filled Black Soul Gem into Atronach Forge box, press lever and you will get random enchantment on this item. Also edits some vanilla recipes for sake of balance.

Requires new game. Requires SKSE. Compatible with anything that doesn't edit AtronachForgeSCRIPT.psc.

Includes Requiem "patch" - ONLY thing it does is, it moves Slighted from Forge to room with Ice Wraith (which is removed). I think it's fair considering that OP recipes were altered.
Place this under Requiem to see edited recipes (notes that mages drop).

New Recipes 

Random Enchantment

• weapon/helmet/gloves/cuirass/boots/shield
• filled Black Soul Gem
• 1 - 4 Void Salts (based on material)
  

Random Spell Tome of same level and school

• Spell Tome
• filled Black Soul Gem
• 1 to 3 Briar Hearts (based on tome level)
  

Disenchant item enchanted by a player

• item to disenchant
• Briar Heart
  

Notes

• Maximum magnitude of Enchantments is weaker than what you can find naturally in game
• Enchantments are deleveled with magnitudes based on item material (or gold value if material is unknown)
• Enchantments are mostly vanilla, with a few new additions
• Enchantment magnitude is automatically balanced on magnitude of ingame enchantments, IE if Requiem edits magnitudes Forge enchantments will be based on requiem values
• Spelltomes can be recycled only once
  

Material levels

• level 1 (1x Void Salts required): Steel, Leather, Iron, Stormcloak, Studded, Imperial, Hide, Wood, Draugr
• level 2 (2x Void Salts required): Clothes, Silver, Orcish, Falmer, Elven, Dwarven, Nordic, Bonemold, Chitin, Scaled, Steelplate, Blades, Vampire, Dawnguard, Forsworn
• level 3 (3x Void Salts required): Glass, Ebony
• level 4 (4x Void Salts required): Daedric, Dragonbone, Stalhrim
  

Spell Tome levels

• level 1 (1x Briar Heart required): Novice, Appretience, Adept
• level 2 (2x Briar Heart required): Expert
• level 3 (3x Briar Heart required): Master
  

   
Edited Vanilla Recipes

• Staff of the Flame Atronach
  

        - old: Fire Salts + Broom + Corundum Ore/Ingot + Greater/Grand/Black Soul Gem
        - new: Fire Salts + Broom + Corundum Ore/Ingot + filled Black Soul Gem

• Staff of the Frost Atronach
  

        - old: Frost Salts + Broom + Moonstone Ore/Ingot + Greater/Grand/Black Soul Gem
        - new: 2x Frost Salts + Broom + Moonstone Ore/Ingot + 2x filled Black Soul Gem

• Staff of the Storm Atronach
  

        - old: Void Salts + Broom + Orichalcum Ore/Ingot + Greater/Grand/Black Soul Gem
        - new: 3x Void Salts + Broom + Orichalcum Ore/Ingot + 3x filled Black Soul Gem

• Scroll of Conjure Flame Atronach
  

        - old: Fire Salts + Roll of Paper + Charcoal
        - new: Fire Salts + Roll of Paper + Charcoal + Ruby/Flawless Ruby/Silver Ruby Ring/Gold Ruby Necklace

• Scroll of Conjure Frost Atronach
  

        - old: Frost Salts + Roll of Paper + Charcoal
        - new: 2x Frost Salts + Roll of Paper + Charcoal + Sapphire/Flawless Sapphire/Gold Sapphire Ring/Silver Sapphire Necklace

• Scroll of Conjure Storm Atronach
  

        - old: Void Salts + Roll of Paper + Charcoal
        - new: 3x Void Salts + Roll of Paper + Charcoal + Amethyst/Flawless Amethyst/Silver Amethyst Ring

• Fire Salts
  

        - old: Salt Pile + Ruby/Flawless Ruby/Silver Ruby Ring/Gold Ruby Necklace + any Soul Gem
        - new: Salt Pile + Ruby/Flawless Ruby/Silver Ruby Ring/Gold Ruby Necklace + filled Common Soul Gem

• Frost Salts
  

        - old: Salt Pile + Sapphire/Flawless Sapphire/Gold Sapphire Ring/Silver Sapphire Necklace + any Soul Gem
        - new: Salt Pile + Sapphire/Flawless Sapphire/Gold Sapphire Ring/Silver Sapphire Necklace + filled Common Soul Gem

• Void Salts
  

        - old: Salt Pile + Amethyst/Flawless Amethyst/Silver Amethyst Ring + any Soul Gem
        - new: Salt Pile + Amethyst/Flawless Amethyst/Silver Amethyst Ring + filled Common Soul Gem

• Conjurer's Elixir
  

        - old: Empty Wine Bottle + Ectoplasm + any Soul Gem
        - new: Empty Wine Bottle + Ectoplasm + filled Common Soul Gem + Briar Heart

Forge only takes required amount of ingredients so you can safely put there higher amount if not sure.
Also savescumming to get the best enchantments is strictly forbidden!