https://divine-pride.net is the most up-to-date resource for looking things up:
Two main builds, Psychic Wave and Diamond Dust. Psychic Wave is the stronger, more versatile build, but is much more expensive to get started. Conversely, DD is pretty easy to get started but is weaker (especially against shadow/holy mobs). PW can also be a bit slower than DD at burst damage since it's multiple smaller damage instances over time, so some mobs might take a few casts or a second to kill.
Common Gear
Common:
King of Spirit Circlet - 100% MDef penetration, good damage multipliers for DD, 70% Fixed Cast Time reduction (FCT), 20% After Cast Delay reduction (ACD), 30% Variable Cast Time reduction (VCT), and 1s Cooldown reduction (CDR) for DD
Circlet of Time (Sorcerer) [1] - Good damage multipliers for DD/PW, neutral/water magic damage multipliers, and can be enchanted with bonus MATK% and FCT reduction
Middle + Lower Headgear:
Sunglasses/Sunglasses [1] + Mob Scarf - Lots of MATK
New Wave Sunglasses + Ghost Fire - Better Mob Scarf Combo for 4th classes
Kardui Ear - Lots of MATK, a bit of VCT
Floating Ball - Even more MATK
Fortunetelling Sealed - Up to 20% size multiplier
Tyrant of Earth/Old Camouflage Scarf - Up to 25% size multiplier
Tree Sprout - Bonus with Kardui for a bit more MATK and VCT
Sacred Lapel - 15% ACD if necessary
Armor:
Automatic Armor Type B (2x Shadow Spell, 1x MATK/Warmer Wave/Global Delay/Diamond Grave) [1] - Best magic armor, I think. Shadow Spell is one of the best options for improving magic damage
Illusion Armor Type B (2x MATK, 1x Global Delay) [1] - Cheaper version of Automatic Armor
Soutane of intelligence (Blessing of intelligence) [1] - Provides lots of MATK and INT
Armor Card:
Sweet Nightmare - MATK and uninterruptible cast
Weapon:
Build-specific
Weapon Card:
Blue Pitaya - Water magic damage multiplier and set bonus with Research Assistant Bot and Bookworm for PW/DD damage multipliers
Wizard of Veritas - Set bonus with Fairy of Eden for lots of INT
Mutating White Knight - Magical size multiplier
Shield:
Excelion Shield [1] - Lots of raw MATK
Mad Bunny Special [1] - Some MATK and uninterruptible cast
Shield Card:
Mutating Khalitzburg - 25% damage reduction from medium/large enemies, and a small set bonus with Mutating White Knight
Garment:
Fairy of Eden [1] - Lots of MATK% and other niceties
Temporal Int Manteau [1] - Lots of MATK. Can get enchanted with -15% ACD
Shoes:
Fifth Element [1] - Lots of MATK and ACD, and possibly INT. Also great utility with Electric Walk
Moaning of Evil Spirits [1] - MATK and MDef pierce
Temporal Int Boots [1] - MATK and some VCT. Runaway Magic is a fairly strong enchant
Temporal Dex Boots [1] - .5s FCT and some VCT. Runaway Magic is a fairly strong enchant
Shoes Card:
Research Assistant Bot - Only useful for the set bonus
Accessory:
Sixth Sense Ring [1] x2 - 30% ACD, Psychic Wave damage multiplier, some magic damage multipliers, and crucially reduces PW cooldown by 1s.
Accessory Card:
Bookworm - PW/DD multiplier, and set bonus.
Shadow:
Sorcerer Shadow Set (Sorcerer Weapon Shadow, Sorcerer Shield Shadow, Sage Shadow Armor, Sage Shadow Shoes, Magician Shadow Earring, Magician Shadow Pendant) - Notably gives +10 all stats and DD bonuses (up to 4s CDR for DD)
PW
Goals: Removing 5s Cooldown, 1s After Cast Delay, and 0.6s Fixed Cast Time (this can be done by summoning Ventus)
5S CD is critical, and requires the full set of 2x Sixth Sense Ring, >+11 Awakened Shadow Staff, Sorcerer Stone (Garment) and Scholar Stone (Lower), which is prohibitively expensive.
Headgear Card:
Plaga - Neutral magic damage multiplier
Weapon:
Awakened Shadow Staff [2] - A bit of PW damage boost, but most notably 1s PW CDR
Garment Card:
Purple Pitaya - 3% neutral magic damage multiplier per upgrade
Accessory Card:
Dy (20% neutral magic damage multiplier) if possible, otherwise just another Bookworm
Costume:
Sorcerer Stone (Garment) + Professor Stone (Lower) - 2s PW CDR
Sorcerer Stone (Upper) - .5s FCT reduction
Sorcerer Stone (Middle) - Bonus with Garment stone for a bit of PW multiplier
Shadow:
Psychic Shadow Armor/Shield/Shoes - PW multiplier
DD
Headgear Card:
Blue Lichtern - Water magic damage multiplier
Weapon:
Deus Ex Machina [3] - Ridiculous amount of MATK%. Also ACD, FCT, and lets you use Blessing
Awakened Chilling Cane [2] - Boosts DD a bunch
Dust Grave [2] - Fairly similar to Awakened Chilling Cane, but I haven't run the numbers yet
Garment Card:
Faceworm Larva - 3% water magic damage multiplier per upgrade
Accessory Card:
Headless Mule - 20% water magic damage multiplier
Costume:
Sorcerer Stone II (Garment) - DD multiplier
Sorcerer Stone (Lower) - DD multiplier and all elemental damage multiplier
Scholar Stone II (Upper) - DD multiplier combined with the Garment Stone
Shadow:
Dust Shadow Armor/Shield/Shoes - DD bonuses
(Sorcerer set works just fine)
Cheaper Gear
Headgear:
Skull Cap - MATK and VCT reduction with Thorn Staff of Darkness
Weapon:
Thorn Staff of Darkness - MATK and ACD. Can be enchanted with Spell enchants for VCT reduction
Thanatos Staff [1] - Spells have a chance of regenerating some HP. Combined with Indulge, lets you sustain forever.
Armor/Garment/Shoes/Accessory:
Noblesse/Imperial/Grace Equipment Sets (see iROWiki for info)
Shoes:
Unslotted Temporal Int/Dex Boots - Strictly worse than the slotter versions, but significantly cheaper
Accessory:
Spirit King's Ring [1] - Most notably 2s CDR for DD and some DD damage multiplier
Closing Remarks
PW is one of the best builds in the game, but gathering all the pieces of Exodia is very hard.
Elemaster doesn't offer much except for Talent Points (SPL is strong) and Spell Enchanting
Conflagration helps a bit with DD by turning non-boss mobs into Fire 1 element
