Gilgamesh is a truly hybrid warrior. He deals good damage both with his abilities and his autos. Despite that in the later stages of the game any ability builds are starting to fall off, so I find it to be the best move to build him hybrid: both with a bit of power and AS.
Winds of ShamashPlanning your build you want it to have a nice synergy with Gilgamesh 1st ability. It deals additional damage every auto according to your maximum HP. So, you want your HP and attack speed to be high to max the damage. Building HP is a good idea - you're becoming harder to kill. Speaking about AS - two items is usually enough to make sure you'll do a good damage to those who will stack in your ultimate or will be kicked into the wall.
Not ConquestAs you know in the Conquest Gilga is usually played as a jungler. Speaking of other game modes I find it a bad idea to build him full damage. In Siege, Arena or Clash you don't have enough space to rotate around the map picking only advantageous fights. There in 5v5 or 4v4 you'll will quickly find Gilga shredded into pieces (of course if you're trying to build him full damage).
Mystical Mail
AURA - ALL enemies within 25 units are dealt 20 (+1.5 Per Level) Magical Damage per second.
Bulwark of Hope
PASSIVE - When you take damage and are below 40% Health, you gain a Shield with health equal to 12% of your Maximum Health for 20s. Can only occur once every 60s.
Berserker's Shield
PASSIVE - While below 60% Health you become Berserk for 5s. While Berserk, you gain 5% Damage Mitigation and 20% Attack Speed. This effect can only occur once every 15 seconds.
Pridwen
PASSIVE - When your Ultimate ability has finished casting, you gain a Shield equal to 90% of your Protections from items and abilities for 5s. When destroyed, by timing out or being depleted, it explodes in a 30 unit radius and deals Magical damage equal to 75% of your Protections from items and abilities and slows targets by 25% for 3s. This can only occur once every 45 seconds.
Qin's Sais
PASSIVE - On Basic Attack hits, deal Physical Damage equal to 1.5% of the target's maximum Health. If the target has over 2000 Health, the bonus damage scales up. This effect reaches a maximum of 6% of the targets Maximum Health at 2750 Health.
Death's Embrace
PASSIVE - Hitting an enemy with a Basic Attack restores 1.4% of your Health, 2% of your Mana and reduces your active non-Ultimate Cooldowns by 0.33s. Basic Attacks that deal damage in an AoE restore less health (75% for Melee Attacks, 50% for Ranged Attacks) for each enemy hit after the first and only count once for the Cooldown reduction effect.
Mystical Mail
AURA - ALL enemies within 25 units are dealt 20 (+1.5 Per Level) Magical Damage per second.
Shogun's Kusari
AURA - Allied gods within 70 units have their Attack Speed increased by 30%.
Berserker's Shield
PASSIVE - While below 60% Health you become Berserk for 5s. While Berserk, you gain 5% Damage Mitigation and 20% Attack Speed. This effect can only occur once every 15 seconds.
Evolved Hide of the Urchin
PASSIVE - Provides a Health Shield that gains stacks every 2s. Shield only stacks if you have not taken or dealt damage in the last 5s. Each stack provides 10% of 100 Health +5 Per Level. The full shield will regenerate after 20 seconds.
Qin's Sais
PASSIVE - On Basic Attack hits, deal Physical Damage equal to 1.5% of the target's maximum Health. If the target has over 2000 Health, the bonus damage scales up. This effect reaches a maximum of 6% of the targets Maximum Health at 2750 Health.
Stone of Gaia
PASSIVE - If you are hit by a Knockup, Knockback, Pull, or Grab you gain 7% of your max Health over the next 5 seconds. You gain 15 Physical Power and 25 Magical Power while this effect is not on cooldown. This effect does not trigger on Vortexes. Can only occur once every 15s. PASSIVE - Regenerates 0.4% of your max health every second.
Spectral Armor *old*
PASSIVE - Physical Critical Strikes bonus damage taken is decreased by 40%.
The Sledge
PASSIVE - For each enemy god within 55 units of you, you gain a stacking buff that provides 10 Physical Protections and 8 Magical Protections. Stacks up to 3 times.
OLD Shifter's Shield
PASSIVE - While over 75% Health, you gain +25 Physical Power. While under 75% Health, you gain +40 Protections.
Hide of the Urchin
PASSIVE - You gain +3 Magical Protection and +3 Physical Protection for each god kill or assist. At 7 stacks this item Evolves, providing a Health Shield that gains stacks every 2s. Shield only stacks if you have not taken or dealt damage in the last 5s. Each stack provides 10% of 100 Health +5 Per Level.
OLD Ancile
PASSIVE - Whenever you take Magical Damage from an enemy ability you unleash a shockwave that Silences all enemies within a range of 30 units for 1s. This effect cannot trigger more than once every 30s.
Blackthorn Hammer
PASSIVE - While over 25% Mana, you gain +10% Cooldown Reduction. While under 25% Mana, you gain +50 MP5.
Runic Shield
AURA - Enemy gods within 55 units have their Magical Power reduced by 50.
Talisman of Energy
PASSIVE - Getting a kill or assist on enemies causes you and allies within 70 units to gain stacks of energy. Energy stacks provide 3% Movement Speed, 3% Attack Speed, and 15MP5 per stack. Lasts 10s and stacks up to 4 times. Killing or Assisting an enemy God provides maximum stacks.
Void Shield
AURA - Enemy gods within 55 units have their Physical Protection reduced by 10%.