NOTE: This is not the EXACT way to play as an evil melee character. Feel free to customize, and even add things in the comments. You can also change whichever ending you want, but I felt that the Legion ending was the most "Evil" one.
Evil - Melee Character Guide
This is my preferred way of an Evil/Melee character for Fallout New Vegas. Feel free to add any advice in the comments/replies. Thanks.
The Beginning - Goodsprings
Anyways, whenever you begin the game and adventure of Fallout New Vegas, you talk with Doc Mitchell, and you name your Courier, etc. Then you choose your SPECIAL.
My Special Setup -
This is my suggested set up, you can of course modify it to your liking.
Strength: 8
Perception: 1+ (going to implant or you can add Intense Training). This is low because you're a melee character, not a sniper.
Endurance: 5
Charisma: 1 (you're an evil bastard, no need for Charisma)
Intelligence: 10 (always a necessity)
Agility: 5 - 8 (depends on your preference)
Luck: 10 (I mainly keep this for criticals, but it is also good for casinos and such)
Skills -
Feel free to change this to your enjoyment. Disperse points evenly.
Barter
Speech
Medicine
Melee Weapons
Repair
Unarmed
Science (optional)
Lockpick (optional)
Starting Perks -
You can take any perks you see fit, but the ones that I took were Good Natured (for speech, barter, and medicine bonuses) and Hoarder (just so that I can carry extra crap to sell)
After the beginning -
Once out of Doc Mitchell's house, head down to Sunny Smiles and initiate the tutorial. Shooting bottles and punching geckos. Whenever you complete the tutorial, head back in to the Prospector's Saloon in Goodsprings and talk to Joe Cobb about taking over Goodsprings. He'll tell you go to shake down stores and the doctor.
After shaking down stores and Doc Mitchell, and killing Ringo, then you go right down and kill everyone in the fine town of Goodsprings. Once you take over Goodsprings, go ahead and kill Joe Cobb and the rest of the powder gangers there. Y'know. Why not.
Off to Primm! -
Once in Primm, head into the Bison Steve and take out all of the Convicts there, making your way to Deputy Beagle. Once you make it to him, go ahead and kill him. Take his journal for the next part of the story, and head out the Bison Steve to the Vicky-Vance Casino.
Walk in, and talk to Johnson Nash. Sell as much as you can until you reach his max amount of caps. Then go ahead and kill everyone in the casino, they aren't important to the story anymore. Loot their items and continue moving. Be sure to stay out of the NCR area on the other side, otherwise they'll attack.
Head down to NCRCF or the NCR camp and get a sheriff for the town of Primm. After you have a sheriff, feel free to kill him.
Nipton -
Anyways, head on to Nipton and find Vulpes. He'll give you the Cold, Cold Heart quest. You don't have to do this, but you can go ahead and fast travel to Mojave Outpost and talk to Ghost on the roof and finish it.
Oh, and be sure to kill Swanick (the guy who goes crazy about winning the Nipton Lottery). Just for fun.
Novac -
Once in Novac, talk to Manny Vargas about the Great Khans, and (if you have Cherchez or Confirmed Bachelor) he'll tell you about Benny. Go down to the dinosaur and talk to Cliff Briscoe. Sell everything that you can to him.
Wait until Night and go back to the Sniper Nest. Talk to Boone about the quest "One for My Baby." Once you have this quest, head into the Dino Dee-Lite front desk and either lockpick the safe, or pickpocket the key from Jenny-May Crawford. Either way, get the Bill of Sale from the Safe and tell Jenny-May to go in front of Dinosaur.
After she is assassinated, head back up into the Sniper's Nest, and collect your reward. Then kill Boone and everyone else in Novac. They aren't important.
Boulder City -
You can actually skip this if you want to head straight for New Vegas, but if you want to rack up some karma with Great Khans, you'll want to do this.
Head to Boulder City and talk to the NCR Lieutenant about the Great Khan incident. Then get the quest "Boulder City Showdown." Head into the ruins and kill all of the Great Khans there, then release the NCR prisoners (or kill them if you want to pick a fight with the NCR).
The quest will automatically end, so no need to worry about talking the to the Lieutenant again.
New Vegas and Beyond! -
After Boulder City and into New Vegas, be sure to do the Legion story arc for the worst ending. Feel free to do whatever you wish, I personally went around every casino and killed everyone I could find (including Securitrons). After you make it into New Vegas, it's up to you to finish.
Anyways, this was my personal Evil/Melee Character. As I said in the beginning, you can change whatever you like, but this is my suggested set up for bad karma and Melee-Special.