All you really need is high speech and/or 75 repair if you are going for fast power armor.

SPECIAL
Doesn't really matter, but I used 10 Intelligence for the purpose of this guide

STR 5
PER 5
END 5
CHR 5
INT 10
AGI 5
LUK 5

TAGED SKILLS

OPTIONAL
Lockpick (makes things slightly more smoother in the Cathedral) starting value: 55%
Repair (if you want to grab Power Armor) starting value: 60%
Outdoorsman (makes traveling the long distances in this route easier) starting value: 42%

REQUIRED FOR THE RUN
Speech (a must) starting value: 80%

TRAITS

Good Natured (you won't need combat skills)
Skilled (you won't need perks)

I lean towards Outdoorsman and just use speech skills to enter/exit the Cathedral areas (which is the only use of lockpicking on this route, although it is less complex, and error prone)

-Leaving the cave, fight or run past all the rats to the exit.
-Head directly EAST to Shady Sands
-Run to the second map of Shady Sands which is to the east
-Enter the house near the brahmin stable and search the book shelf in the room behind to curtins to grab some rope (and a wilderness guide) Alternatively enter the small house near the crops and their is some rope on the floor (pixel hunt)
-There is a second wilderness guide on a bookshelf in the house to the left of the town gate (helps to boost outdoorsman)
-Leave Shady Sands

-Travel far southwest to the L.A. Boneyards (it is almost directly south of Vault 13)
-After talking with the gate guard (forced) just ask to enter, then enter the second map which is directly behind you.
-Run WEST to enter another map and the location of the Childern of the Apocalypse.
-Enter the large house and find the room with 3 purple robes laying on the ground: grab one and don it immedately. (might as well)
-Search the ice box up in the adjacent room for some RAD X. (and stim packs)
Leave the Boneyards.

-Travel SOUTHEAST until you reach The Glow
-Upon arrivel immediately pop some RAD X to counter the high radiation
-Use the rope to descend into the giant hole
-Once inside, run around the hole to the other side and loot the Power Armor corpse
-Grab the holodisk tape
-Leave The Glow

-Travel to the Brotherhood of Steel bunker which is to the Northwest of the Boneyard.
-Talk to the guard on the LEFT and ask to join. Accept his "suicide" quest.
-Talk to him again to give him the holodisk to instantly complete the quest.
[LEVEL UP] Optional level Repair to 75 (for Power armor) Required level Speech to at least 96% (100% is safer) to pass all late game checks (Getting the badge/key from Lasher and convincing the Master that mutants are sterile without him just deciding to murder you on the spot)
-Enter the Brotherhood bunker
-Take the elevator to LEVEL 3
-Talk to Vree the head scribe
-Ask about technical information then mutations to learn about mutants being sterile, then ask for proof to recieve a holodisk tape. Use the holotape.

OPTIONAL FOR POWER ARMOR.
At this point this is quickest way to obtain power armor without any combat

-Level repair to at least 75 (having it taged with 1 level up is enough)
-Talk to Kyle on LEVEL 3 near a table with pieces of broken power armor
-Ask what he does and and learn that he repairs stuff. Inquire about power armor to get a quest to fix the power armor.
-Go to LEVEL 1 and speak to Micheal outside the training room to ask for the part needed. Choose the first option then the last option to obtain the missing piece. NOTE: If you never spoke to him before, you must talk to him twice to get the option. Also becareful here. If you choose the wrong option or end conversation before asking for the component when the option is available you are out of luck
-Go back to LEVEL 3 and give Kyle the missing piece. He will give you a Electronic book to boost repair. Your repair must be at 75 to succeed.
Use repair on the table to get Power Armor.
NOTE: It is dropped on the ground and you will need the strength to pick it up. Stash your stuff in the lockers and try again if you can't lift.

-Travel to The Cathedral just south of the Boneyard
Enter and talk to Lasher in the top left room.
-Ask to talk to the man in charge and inquire about getting past the nightkin. He will give you a badge
-Use the badge on the top right door to unlock it and go up the stairs to floor 3. Alternatively if you have high lockpick, you can simply pick the lock on the door.
-Talk to Morpheus and ask about making a deal. Tell him you have information about his enemies and want to see the master, then mention you are a Vault Dweller and press further and he will take you directly to The Master
-Talk to the Master until you can ask about his plan involving mutants. Mostly the top option. Drop the truth bomb that the Mutants are sterile. Give him the proof. At first he won't believe you even after giving the proof. Choose the second option to reaffirm. Alternatively you can have him ask one of his mutants if your speech is high enough. (Not tested with this route)
He will trigger a 300 second silent self-destruct countdown. You should still be wearing those purple robes. Get the hell out of there. Use the elevator.
-Once you reach the top floor, use science (55%) on the computer console to learn the location of the military base and [LEVEL UP].
At this point if you tagged lockpicking, increase it to 100% and you can talk your way past the vault gate mutant and pick the locked door that is up the stairs using the lockpick tools you start with in order to leave. If not, stand near the purple robed guy, then take off your robe which should immedately initiate conversation. This part is a little tricky as choosing the wrong options result in combat. Spin a story about how you followed a suspcious person down here and you want to leave. Bottom dialog options twice, then the top dialog option. He will immiedately send you outside the Cathedral.
-Leave the Catherdral grounds to watch it die in a nuclear explosion. [LEVEL UP]

OPTIONAL
At this point if you take a detour to Necropolis and talk to Set, the leader of the ghouls (as long as you were quick enough so the Mutants haven't invaded and kill everyone there yet), he will have new dialog since the Master is dead, and he will reward you with a bunch of stuff.

Also if you do this, it is worth talking to the Mutant at the watershed for a shortcut to the Military Base bypassing the need to travel there.

-At this point I like to level Outdoorsmen to 100% so traveling to the Military base is easy. (If the Necropolis shortcut is not used)
-Travel to the northwest corner of the map to find the Military base
-Approach the Mutant sentry. He will ask you to surrender. If you are wearing the purple robes you can get past but it is much faster to ask to be taken to his master
-Talk with the Mutant leader and do not cooperate. When the conversation ends and he tries to punch you, simply run away. Run through the red force field to the northen room with robed figures. Use your computer skill on the console with colored screens. (This might take several attempts) Once you get text that says you've managed to switch the computer to an Interface, simple then use the computer console.
-Choose the second to bottom code to activate the 300 second silent self-distruct sequence.
Take the elevator on the left to the 3rd floor
-Run through the prison block and talk your way past the mutant (easy when wearing purple robes)
Take the next elevator to the top floor
-Run to the exit
-The mutant sentries outside will stop you again, choose the bottom option to get past them using your purple robe status
-Leave the Military Base to watch it die in a nuclear explosion...thus triggering the end game.