The main thing the build will be centered around is critical hit chance, as well as VATS centered combat. The other option is to focus more on stealth combat which also works effectively. Almost anything goes in a Luck build but the best are Pistols, One Handed Melee, Energy Weapons, and Some Rifles. If there is anything you think I missed or should add please comment!

Use what you have access to and what you prefer


Lucky Shades - +1 Luck, +3 Perception (Only with Four Eyes trait) - DT 0

1st Recon Beret - +5% Critical Chance, +1 Perception - DT 0

Naughty Nightwear - +1 Luck, +10 Speech - DR 0

Courier Duster (Blackjack Variant) - +1 Luck, +30% Poison Resistance - DT 13 (The Blackjack Variant can only be obtained if sided with Yes Man and have completed the Lonesome Road DLC)

Armor of the 87th Tribe - +10 AP, +3% Critical Chance, +1 Charisma - DT 22

Elite Riot Gear - +5% Critical Chance, +10 Guns, +1 Charisma - DT 22

Elite Riot Gear Helmet - +2 Perception, +5 Speech, Sneak Sight - DT 6

Ulysses' Duster - +5% Critical Chance, +1 Charisma - DT 13

Joshua Graham's Armor - +3% Critical Chance - DT 15

Salt-Upon-Wounds' Helmet - +2% Critical Chance, +5 Sneak - DT 4

Marked Beast Face Helmet - +2% Critical Chance, +3 Melee Weapons - DT 3

Use what you have access to and what you prefer


Lucky - Requires Strength 3. Uses .357 Magnum. It is a very effective weapon for a Luck build because of its high fire rate, high critical chance, and only uses 17 action points in VATS. Comes pre-installed with long barrel weapon mod. Is a holdout weapon as long as you have a sneak of 50. It is located in the Bison Steve Hotel inside of a locked floor safe which requires a Lockpick of 75 to open.

Paciencia (GRA) - Requires Guns 50 and Strength 6 (Not really available with base SPECIAL I gave so you will have to get an implant from Dr. Usanagi or something similar). Uses .308. It has really high critical damage of 110 points which is the same as the anti-material rifle. Critical Hits are way more common. Has max scope weapon mod pre-installed. Can be bought from Cliff Briscoe at Novac or Gun Runners if Cliff Briscoe is dead.

Love and Hate - Requires Unarmed 50 and Strength 3. Is a holdout weapon by default regardless of Sneak skill. Found on a Viper Gang Leader at Bonnie Springs.

Chance's Knife - Requires Melee Weapons 50 and Strength 3. Is a holdout weapon if your sneak is 50. Can be found in Chance's Grave near Tribal Village (Requires a shovel to dig up).

Q-35 Matter Modulator - Requires Energy Weapons 25 and Strength 2. Uses Microfusion Cells, Heavy Energy Cells, Plasma Cartridges, and Plasma Cores. Is a direct upgrade from the normal plasma rifle in every way. Uses 2 less Action Points in VATS. 15% More critical damage. It's located on the main floor of the REPCONN headquarters behind a 100 Lockpick door or 100 Science terminal or the keycard on the third floor or the room right above behind a Lockpick 75 door through a hole in the ground.

AER14 prototype - Requires Energy Weapons 25 and Strength 3. Uses microfusion cells. This is the best laser rifle variant, it has the highest critical hit chance and critical hit damage of any laser rifle. Has a unique green laser instead of red. It is located inside Vault 22, in the common area. Go to the fifth floor, pest control, and enter the stairway door to the common area which is to the right upon exiting the elevator; it has a lock with a difficulty that varies according to the player's level. The AER14 is lying on the ground next to a scorched skeleton. It is possible that a companion will pick it up. If the weapon is not present near the skeleton, check the inventory of all companions. With the right skills and stats it is possible for this weapon to reach 95% critical hit chance.

Ratslayer - Requires Strength 3. Uses 5.56mm. It is a unique variant of the Varmint Rifle that is lighter, has a higher DPS, a much higher critical multiplier, and can use all normal varmint rifle weapon mods. It is located inside the Broc Flower Cave, below a desk in the lab on the upper level.

Alien Blaster - Requires Energy Weapons 75. It is a guaranteed critical hit on any hit. It uses Alien power cells. It is found north of Horowitz Farmstead. Can only be found if you have the Wild Wasteland trait.

Abilene Kid LE BB Gun - A unique variant of the normal BB gun that has a higher critical hit chance and really high critical damage bonus. Uses BB's. Default it has 70 added critical hit damage but if you have the perks Better Criticals and Just Lucky Im Alive it can do 157 critical hit damage. The Finesse perk is a good idea to use with this. It's only really a good idea to use this weapon in a stealth build. It can be found in Fields Shack unless you have the Wild Wasteland trait then when Rex is a companion he will say "aroo" and ask him if someone fell down a well.

Any other weapons should work fine but I highly recommend the weapons above.

SPECIAL


Strength - 3

Perception - 7

Endurance - 4

Charisma - 2

Intelligence - 6

Agility - 7

Luck - 10

(There are comments below of others that disagree with these, please read those and decide what you want to assign from there, mainly because of the implants that you can get so feel free to swap these points around for whatever works best for you)

Traits


Built to Destroy - +3 Critical Chance but +15% Faster Weapon Wear

Wild Wasteland - Certain items can only be found with this trait that will help with the build

Claustrophobia and Early Bird - I do not recommend getting either of these two traits but if you want to get them its entirely up to you.

These are not all required just choose what perks work for you.


Enhanced Sensors - Enemies are easier to detect and target, even while cloaked. Requires ED-E as a companion.

Spotter - Enemies highlighted while sights are aimed down or zoomed in. Requires Craig Boone as a companion.

Light Touch - +5% Critical Chance, enemies suffer -25% Critical Chance. (Only while wearing light armor). Requires Agility 6, Repair 45, and Level 2.

Gunslinger - One handed weapons chance to hit in VATS is increased by 25%. Requires Level 6.

Commando - Two handed weapons chance to hit in VATS is increased by 25%. Requires Level 8.

Sneering Imperialist - +15% Damage and x1.25 multiplier for VATS hit chance to those of raider, junkie, and tribal "races". Requires Level 8

Math Wrath - Reduce all Action Point costs by 10%. Requires Science 70 and Level 10.

Fight the Power! - +2 Damage Threshold and +5% critical chance against any person wearing NCR, Legion, or Brotherhood of Steel faction armor. Requires Level 10.

Finesse - Higher critical hit chance (equivalent to +5 Luck). Requires Level 10.

Mysterious Stranger - 10% Chance he will come to finish off enemies in VATS. Requires Luck 6 and Level 10.

Miss Fortune - 10% Chance she will come to cripple and knockdown enemies in VATS. Requires Luck 6 and Level 10.

Plasma Spaz - Action Point costs for all plasma weapons are reduced by 20%. Requires Energy Weapons 70 and Level 10.

Hobbler - The chance to hit legs in VATS is increased by 25%. Requires Perception 7 and Level 12.

Sniper - The chance to hit the head in VATS is increased by 25%. Requires Perception 6, Agility 6, and Level 12.

Center of Mass - When targeting the torso in VATS, an additional 15% damage is done. Requires Guns 70 and Level 14.

Action Boy/Action Girl - Extra 15 Action Points for VATS. Has 2 ranks. Requires Agility 6 and Level 16.

Better Criticals - +50% damage with critical hits. Requires Perception 6, Luck 6, and Level 16.

Concentrated Fire - Chance to hit any body part in VATS increases slightly with each subsequent hit on that body part. Requires Guns 60, Energy Weapons 60, and Level 18

Paralyzing Palm - 30% chance to perform a special VATS palm strike that paralyzes your opponent for 30 seconds when using unarmed weapons. Requires Unarmed 70 and Level 18.

Grim Reaper's Sprint - If you kill a target in VATS, 20 Action Points are restored upon exiting VATS. Requires Level 20.

Ninja - +15% critical chance with Melee or Unarmed attacks. Sneak Attack Criticals do 25% more damage. Requires Sneak 80, Melee Weapons 80, and Level 20.

Laser Commander - +15% damage and +10% chance to critically hit with any laser weapon. Requires Energy Weapons 90 and Level 22.

Nerves of Steel - Increases the regeneration speed of Action Points by 20%. Requires Agility 7 and Level 26.

Meat of Champions - +1 to Luck, Intelligence, Charisma, and Strength for 60 seconds after eating a corpse. Obtained by eating the bodies of Caesar, Mr. House, The King, and President Kimball (Requires the Cannibal perk).

Just Lucky I'm Alive - Whenever you finish a fight with less than 25% health, your Luck temporarily increases by +4 for 3 minutes. The perk also permanently increases your own critical hit damage +50%, as well as grants permanent immunity to critical hits that you would otherwise receive. Requires Neutral Karma and Level 50.

Set Lasers for Fun - Increases critical hit chance with energy weapons by 2 percent every rank (max 4, only 2 ranks). Unlocked by completing the challenge of the same name, you must deal 16,000 damage with pistol grip energy weapons for one rank and 25,000 damage with the rifle grip energy weapons for the other.

True Police Stories - Consumable skill magazine found in various locations, reading one increases your critical hit chance by 5% (10% with the Comprehension perk) for 60 seconds (180 seconds with Retention. Can also be crafted using 1 Wonderglue and 2 Blank Magazines (Requires repair 25).