Start your game without any DLCs. The DLC content kicks in at higher levels, and for each DLC there's a pop-up notification which slows you down.

• Your character must be a woman.
  
• Set Strength to 1. You won't have time to pick up things anyway, and melee combat is too slow.
  UPD: it's good to have at least ST 3 for the finale - to run in power armor
  
• Set Charisma to 10. You'll need Speech or Barter skill at 100 for the endgame.
  
• Set Intelligence to 10, it gives extra skill points.
  
• Set Agility to 1. The running speed does not depend on Agility value, and you'll need extra points. Action Points are not useful outside V.A.T.S.
  
• You can set Luck to 9, it gives +5 to all skills. Critical hits are also good because you'll be an awful shooter anyway. But that's optional.
  
• You must tag Speech skill.
  
• Take the Good-Natured trait. Also an awful shooter, a perfect speechwoman.

The rest is for your liking. For tagged skills, I also recommend Guns and Sneak.

Here's my optimized stats and another build with Early Bird (not a good option because the endgame comes at evening):

Talk to Doc Mitchell as soon as you can get up; you'll reach the door faster than him. Also you can loot his house for stimpaks while he's walking and talking during the whole scene.

Ah, the smell of fresh air. I presume you already know where exactly is New Vegas, right?
Outside Doc Mitchell's house run to Goodsprings cemetery. It's the only hill to the left of you.

UPD: turns out, the shorter route would be run to Camp McCarran through the Hidden Valley and Power Substation, and then fast-travel to Goodsprings Cemetery and run to the Red Rock Canyon from there, then fast-travel. That way you won't have to run to Hidden Valley and Substation again. But I've not tested this yet.

Run to the big water tower, and down from there to the road:


It's a good idea to save at the marked point.

Now's the tricky part. You'll need to run past several Cazadores, Deathclaws and some high-level bandits. On Very Hard difficulty, you'll be dead in one sting. Basically, you should avoid cazadores by running higher, and avoid deathclaws by running lower (cazadores would lose interest in you at this point), and avoid bandits by running farther from them. Also you can lure deathclaws to deal with the bandits and outrun all of them. High Endurance also helps, but not much: you're still a meat for the claws. See my screens (Very High / Hardcore):


Now run to the Red Rock Canyon while you're around. You need just to visit it, and when you've discovered the location, you're done. Get out.

Run to Camp McCarran - it's a wild chase, but Vipers and geckos are nothing compared to who you've already outrunned. Also, you have stimpaks. Try to run past some landmarks, it will save you some walking to the El Dorado Substation later. The safest route is Samson Rock Crushing - Basincreek Building - McCarran. It's also the longest, so try to find a balance.

Second floor, left wing. A word 'MONORAIL' written in big letters there. They'll try to stop you, but you are a natural runner, and once you're inside the Strip, no one seems to care about you anymore.

You're out NCR embassy, and then Victor shows up. He's impossible to dodge, he forces you into a dialog even in mid-air, so just click through the answers. Screw Mr. House, let's go gambling.

When you enter the Tops, ask the man at the reception about Benny. This gives you some XP. Then go and see Benny, this gives you even more XP. You'll automatically advance several levels at once. Do not engage him, you need those levels first. Take Black Widow perk (see why your character had to be a woman?) and advance your Speech skill. Walk to Benny, use your new perk, love him, kill him in his sleep. Poor Benny.

Okay, now Ben is dead, you're level 4 (that's some crazy experience) and you have another perk. You're free to choose, I took Swift Learner.

Now it's a highway to the ending. Independent Vegas is the fastest option because you can just ignore everyone and make yourself the Boss.

Steal Maria from Benny (that's his pistol) and talk to Yes Man. You can tell him Khans are harmless right away.

Now rush to Ultra-Luxe (yes, NCR and Caesar messengers are in the way, we'll get them killed later) and talk to Mortimer (door across the hall).

Note: if you're playing on Hardcore, drink from the fountain now. Next stop for a sip will be only at Hoover Dam.

Hooray, that's it for White Gloves, Now talk to receptionist at Gomorrah, say bye to Omertas and go kill Mr. House.

You know how to kill Mr.House, right? New Vegas is not for pacifists; in fact, you can finish the game with only one kill - and sadly, Gregory House is the victim. Jump, run, pray and disable him - that's it.

Now: Boomers. Walk out the Strip and cross Freeside, then run to Boomer camp. It's insanely hard to get past the howitzers (especially when you're still level 5), especially on Hardcore because if you cripple anything - there's no one here to heal you, stimpaks won't work, and even at Goodsprings you still need 50 caps to get treatment. It's especially painful if you cripple your legs.

If you're still alive after that, you meet Pearl and that's it for this tribe.

Unfortunately, there are deathclaws between McCarran and Hidden Valley, so your best bet for fast travel is Goodsprings Cemetery. From there, run to Yangtze Memorial, then Hidden Valley. Finding The Bunker is entirely up to you.

Equip Maria and shoot the Brotherhood paladins. Run like hell so you won't have to do their long and tedious entrance quest. Fast travel to the Strip (North Gate, I presume) and finish the quest the most ignorant way. Your dead lover is still there, but you can't fix that.

Now you're one happy sole owner of the best casino in town, the Lucky 38. And you're completely out of money. And that's just a day after you've emerged from a grave.

While you're watching the presentation, grab and equip 9mm submachine gun. You can equip it and take ammo while Yes Man's talking. It will help you at the Dam in case someone jumps at you in narrow corridor.

You shouldn't care what happens with Kimball, but the El Dorado Substation business sounds serious.

Fast travel to Samson Rock Crushing Plant, Basincreek Building or Camp McCarran if you were cutting corners previously. Hidden Valley seems like a faster option, but it's not: it's nearly impossible to cross Black Mountain on fifth level. Certainly not faster and you have no stims now.

From Basincreek, it's strictly southeast but some Vipers are in the way, and they're well armed. Run to the east past a building, then southeast. South from the first power tower. Follow the power lines.

A woman runs south. What's on her mind? Probably just another loony.

At the substation, your reputation with NCR should be still rather good, so straight up run into the building and do your job, then fast travel as soon as you're out. They won't have time to react.

Ta-da! New level! Entirely for your liking at this point. I chose Toughness perk and upgraded my Medicine. Sneak is useless now, Guns.. you won't have time for shooting, but Medicine gives you health points and that would really come in handy.

Report to your buddy, and get into epic battle for Hoover Dam.

You can bypass more or less safely the beginning of the road by keeping left side. Use cover and distract enemies with your killer robot buddies, run to the water. Drink it if you like then use a manhole to jump back on the road. Run straight to the door, you should have a quest marker.

Take an elevator down, then run to the Control Room. There're two heavy guards there. Don't move in the room - they'll get hostile and then you're certainly dead. You can just talk to them and pass a Speech check. There is a way to kill them both on your low level, but it's time-consuming so no heavy armor for you.

Anyway. Install the override chip and run to the exit.

Inside the power plant turn left immediately and blow everything up. Backtracking should be piece of cake since you're still only Shunned for the NCR; don't bother to kill anyone.

Don't go outside yet. Exit the tower by ladder, to appear on top of it; that way you're safe when Legion Centurions will be distracted by your robot buddies. Watch the first 4 seconds of the battle and you may descend to run past them.

In the Legate's Camp, run. You should avoid running close to guards but they're all melee and not a good runners, and you have the Salvaged Power Armor, so sprint straight to the end dialogue.

There was no time to collect magazines, so Speech 100 is absolutely required to bypass the final battle. Check your skills and all the effects - for example, Early Bird trait will be a nuisanse.

And - voila! You've conquered New Vegas!