Optimal enchantment order[Up to 1.21]

All order stated below is based on least penalty strategy for best higher version compatibility(e.g. new enchantments added), as enchanting attempt is limited.
If high version compatibility, or more trivially, renaming cost(renaming before enchanting is recommended), is not important, the enchanting cost can be even lower in some cases.

Description：

1.enchant items in order
2.combine books inside brackets first
3.addition sign means combine the second books to the first book

Trident：
(Loyalty+Channeling)
1.Impaling V
2.Channeling+Loyalty III
3:Unbreaking III+Mending
(3 Prior Work Penalty, Highest exp level:10, Total exp level:33)

(Riptide)
1.Impaling V
2.Unbreaking III+Mending
3.Riptide III

(3 Prior Work Penalty, Highest exp level:10, Total exp level:28)

Crossbow：

(Multishot)
1.Unbreaking III
2.Multishot+Mending
3.Quick Charge III
(3 Prior Work Penalty, Highest exp level:6, Total exp level:17)

(Piercing)
1.Piercing IV
2.Quick Charge III+Mending
3.Unbreaking III
(3 Prior Work Penalty, Highest exp level:7, Total exp level:19)

Bow：

(Infinity)

1:Power V
2:Infinity+Unbreaking III
3:Punch II+Flame
(3 Prior Work Penalty, Highest exp level:10, Total exp level:29)

(Mending)

1:Power V
2:Punch II+Mending
3:Unbreaking III+Flame

(3 Prior Work Penalty, Highest exp level:9, Total exp level:26)

Sword：

(maxed out)

1:Sweeping Edge III
2:Looting III+Sharpness V/Smite V/Bane of Arthropods V
3:(Fire Aspect II+Unbreaking III) + (Knockback II+Mending)

(3 Prior Work Penalty, Highest exp level:17, Total exp level:52)

(no knockback and fire aspect)

1:Sweeping Edge III
2:Looting III+Unbreaking III
3:Sharpness V/Smite V/Bane of Arthropods V+Mending
(3 Prior Work Penalty, Highest exp level:11, Total exp level:33)

Mace：

(Breach)

1:Breach IV
2:Wind Burst III+Unbreaking III
3:Fire Aspect II+Mending
(3 Prior Work Penalty, Highest exp level:11, Total exp level:34)

(Smite/Density)

1:Wind Burst III
2:Density V/Smite V/Bane of Arthropods V+Unbreaking III
3:Fire Aspect II+Mending
(3 Prior Work Penalty, Highest exp level:10, Total exp level:31)

Fishing rod：

1.Luck of the Sea III
2.Unbreaking III+Mending
3.Lure III
(3 Prior Work Penalty, Highest exp level:9, Total exp level:24)

2 enchantments only items(elytra, shield ,etc.)：
1:Unbreaking III
2:Mending
(2 Prior Work Penalty, Highest exp level:3, Total exp level:6)

Axe：

Fortune:

1:Fortune III
2:Efficiency V+Unbreaking III
3:Sharpness V/Smite V/Bane of Arthropods V+Mending
(3 Prior Work Penalty, Highest exp level:11, Total exp level:32)

Silk Touch:

1:Efficiency V
2:Sharpness V/Smite V/Bane of Arthropods V+Unbreaking III
3:Silk Touch+Mending

(3 Prior Work Penalty, Highest exp level:10, Total exp level:30)

Pickaxe/Shovel/Hoe：

Fortune:

1:Fortune III
2:Unbreaking III+Mending
3:Efficiency V

(3 Prior Work Penalty, Highest exp level:8, Total exp level:23)

Silk Touch:

1:Efficiency V
2:Unbreaking III+Mending
3:Silk Touch

(3 Prior Work Penalty, Highest exp level:7, Total exp level:21)

Helmet：

Blast Protection, Thorns

1:Thorns III
2:Blast Protection IV+Unbreaking III
3:(Respiration III+Aqua Affinity) + Mending
(3 Prior Work Penalty, Highest exp level:16, Total exp level:49)

Blast Protection

1:Blast Protection IV
2:Respiration III+Aqua Affinity
3:Unbreaking III+Mending
(3 Prior Work Penalty, Highest exp level:10, Total exp level:31)

Other Protection, Thorns

1:Thorns III
2:Respiration III+Unbreaking III
3:(Protection IV/ Projectile Protection IV/Fire Protection IV+Aqua Affinity) +Mending
(3 Prior Work Penalty, Highest exp level:14, Total exp level:45)

Other Protection

1:Respiration III
2:Protection IV/ Projectile Protection IV/Fire Protection IV+Aqua Affinity
3:Unbreaking III+Mending
(3 Prior Work Penalty, Highest exp level:9, Total exp level:27)

Chest+Leggings(NO Swift Sneak):

Blast Protection, Thorns

1:Thorns III
2.Blast Protection IV+Mending
3:Unbreaking III
(3 Prior Work Penalty, Highest exp level:12, Total exp level:32)

Blast Protection

1:Blast Protection IV
2:Unbreaking III+Mending
(2 Prior Work Penalty, Highest exp level:8, Total exp level:17)

Other Protection, Thorns

1:ThornsIII
2.Unbreaking III+Mending
3:Protection IV/Projectile Protection IV/Fire Protection IV
(3 Prior Work Penalty, Highest exp level:12, Total exp level:28)

Other Protection

1:Protection IV/Projectile Protection IV/Fire Protection IV
2:Unbreaking III+Mending
(2 Prior Work Penalty, Highest exp level:7, Total exp level:13)

Leggings(Swift Sneak):
Blast ProtectionThorns

1:Swift SneakIII
2.ThornsIII+Mending
3:Blast Protection IV+Unbreaking III
(3 Prior Work Penalty, Highest exp level:16, Total exp level:48)

Blast Protection

1:Swift SneakIII
2:Blast Protection IV
3:Unbreaking III+Mending
(3 Prior Work Penalty, Highest exp level:12, Total exp level:32)

Other Protection, Thorns

1:Swift SneakIII
2.ThornsIII+Mending
3:Protection IV/Projectile Protection IV/Fire Protection IV+Unbreaking III
(3 Prior Work Penalty, Highest exp level:16, Total exp level:44)

Other Protection

1:Swift SneakIII
2:Protection IV/Projectile Protection IV/Fire Protection IV+Mending
3:Unbreaking III
(3 Prior Work Penalty, Highest exp level:12, Total exp level:28)

Boots：

【Hint：the position of Protection IV/ Projectile Protection IV/Fire Protection IV/Frost Walker II/Feather Falling IV can be swapped arbitrary】
【Hint：the position of Thorns III/Soul Speed III can be swapped arbitrary】

No Soul Speed：

Blast Protection, Depth Strider, Thorns

1:Thorns III
2:Blast Protection IV+Feather Falling IV
3:(Depth Strider III+Unbreaking III)+Mending
(3 Prior Work Penalty, Highest exp level:17, Total exp level:53)

Blast Protection, Depth Strider

1:Blast Protection IV
2:Depth Strider III+Unbreaking III
3:Feather Falling IV+Mending
(3 Prior Work Penalty, Highest exp level:11, Total exp level:34)

Other Protection, Depth Strider, Thorns

1:Thorns III
2:Depth Strider III+Feather Falling IV
3:(Protection IV/ Projectile Protection IV/Fire Protection IV+Unbreaking III)+Mending
(3 Prior Work Penalty, Highest exp level:16, Total exp level:49)

Other Protection, Depth Strider
1:Depth Strider III
2:Protection IV/ Projectile Protection IV/Fire Protection IV+Unbreaking III
3:Feather Falling IV+Mending
(3 Prior Work Penalty, Highest exp level:10, Total exp level:30)

Blast Protection, Frost Walker, Thorns

1:Thorns III
2:Blast Protection IV+Feather Falling IV
3:(Frost Walker II+Unbreaking III)+Mending
(3 Prior Work Penalty, Highest exp level:15, Total exp level:51)

Blast Protection, Frost Walker

1:Blast Protection IV
2:Frost Walker II+Feather Falling IV
3:Unbreaking III+Mending
(3 Prior Work Penalty, Highest exp level:10, Total exp level:33)

Other Protection, Frost Walker, Thorns

1:Thorns III
2:Frost Walker II+Feather Falling IV
3:(Protection IV/ Projectile Protection IV/Fire Protection IV+ Unbreaking III)+Mending
(3 Prior Work Penalty, Highest exp level:15, Total exp level:47)

Other Protection, Frost Walker

1:Frost Walker II
2:Protection IV/ Projectile Protection IV/Fire Protection IV+Feather Falling IV
3:Unbreaking III+Mending
(3 Prior Work Penalty, Highest exp level:10, Total exp level:29)

With Soul Speed：

Blast Protection, Depth Strider, Thorns

1:Thorns III
2:Soul Speed III+Depth Strider III
3:(Blast Protection IV+Feather Falling IV)+ (Unbreaking III+Mending)
(3 Prior Work Penalty, Highest exp level:23, Total exp level:74)

Blast Protection, Depth Strider

1:Soul Speed III
2:Blast Protection IV+Feather Falling IV
3:(Depth Strider III+ Unbreaking III)+Mending
(3 Prior Work Penalty, Highest exp level:17, Total exp level:53)

Other Protection, Depth Strider, Thorns

1:Thorns III
2:Soul Speed III+Feather Falling IV
3:(Depth Strider III+Protection IV/ Projectile Protection IV/Fire Protection IV)+ (Unbreaking III+Mending)
(3 Prior Work Penalty, Highest exp level:21, Total exp level:68)

Other Protection, Depth Strider

1:Soul Speed III
2:Depth Strider III+Feather Falling IV
3:(Protection IV/ Projectile Protection IV/Fire Protection IV+Unbreaking III)+Mending
(3 Prior Work Penalty, Highest exp level:15, Total exp level:49)

Blast Protection, Frost Walker, Thorns

1:Thorns III
2:Soul Speed III+Feather Falling IV
3:(Blast Protection IV+Frost Walker II)+ (Unbreaking III+Mending)
(3 Prior Work Penalty, Highest exp level:23, Total exp level:70)

Blast Protection, Frost Walker

1:Soul Speed III
2:Blast Protection IV+Feather Falling IV
3:(Frost Walker II + Unbreaking III)+Mending
(3 Prior Work Penalty, Highest exp level:15, Total exp level:51)

Other Protection, Frost Walker, Thorns

1:Thorns III
2:Soul Speed III+Feather Falling IV
3:(Protection IV/ Projectile Protection IV/Fire Protection IV+Frost Walker II)+ (Unbreaking III + Mending)
(3 Prior Work Penalty, Highest exp level:19, Total exp level:66)

Other Protection, Frost Walker

1:Soul Speed III
2:Feather Falling IV+Frost Walker II
3:(Protection IV/ Projectile Protection IV/Fire Protection IV + Unbreaking III)+Mending
(3 Prior Work Penalty, Highest exp level:15, Total exp level:47)