Best beginning Stats?

The ones that reflect the way you can play your character best. There isn't such a thing as 'best stats' in Fallout.
 
agreed, 'best' is at best simply what reflects your personal playingstyle most.
 
this game is nearly impossible to lose as long as you save. the only way a char is terrible in my honest opinion is if they dont have enough STR to carry anything (1 -3 str) or they dont have enough action points to handle combat situtations (1-5 agi).

now if you have already played through the game with a normal charecter who uses guns might i suggest you try a melee weapon charecter. 6+ strength. 9 agility. high endurance. you should have some luck int cha but you dont NEED them. perception can be 1 i think. choose fast shot and if you want to gifted. unarmed and melee weapons tagged, maybe speech as well. perks of toughness, action boy, the free movement one and my all time favorite, SLAYER which makes every hit you do in melee a critical. i do believe there might be a perk that reduces the cost of fighting with your hands by 1 action point, if my memory serves that will let you stab or punch people (with power glove) for one action point only, and use a sledgehammer with 2 points. you will kill everything before it has the chance to attack you twice. due to this build being too abusive i used to gimp it myself by wearing lousy armor like leather jacket or robes. let me know what you think and happy killing.

p.s. this build wont be as fun if you havent had the experience of using guns in this game.
 
While there are truly no "best" stats to play Fallout with, there is what I have found to be a decent sort of "minmax" build for a character who can do the most and kick lots of ass. Good if you like to do the most possible things but not necessarily an easy start.
The numbers require the traits Gifted and Small Frame. Hence not an easy start.
ST6 - enough to carry a little bit, do a little damage, and weild most weapons. You can hit 10 by endgame. Drop this to 5 for a bigger challenge, you can still hit 10 and put the extra point where it suits you, I'd take LK.
PE8 -because you want to hit what you aim at and notice things.
EN4 -closest thing to a trash stat in the SPECIAL system. You don't need more than this.
CH6 -enough for 3 NPCs and you can get more easily.
IN8 -Makes up for the low skill points from Gifted, also one of the more important stats. You can hit 10 by the end of the game and you want to.
AG10 -because being able to shoot twice in a round is a HUGE advantage at the begining of the game.
LK6 -this is not the trash stat of the system. In fact it's pretty good. If you put the extra point from ST here you can hit 10 by the end of the game.
 
As many people have stated above there is no single character build that is so overwhelmingly superior to all others that it should be the only way to go. So there goes my shot for a well thought out character giving you the ability to cover most of the game's attribute checks and quests.
ST5 - ST10 is within your grasp.
PE8 - Pretty good attack bonus and you pass most PE checks, should you need more for "checks" drugs are the way to go. Btw matches the requirements for the "weapon of mass destruction" namely the "Sniper" perk.
EN4 - This is your "converging on uselessness" attribute, should you need more for perks or checks do the Buffout.
CH6 - +1 using Shades and more with Mentats if you need 4th NPC. Obtaining 10 is out of question since you would probably need to invest more invaluable character points or perks would be a waste. (Unless of course you don't mind heavily exploiting the game which would be rather pointless with all those chareditors around). Now, allow me to elaborate on the number of NPCs: My primary strike team includes myself (n/c), Vic, Cassidy, Sulik, Brain bot. 5th would be Marcus but then again I believe you are giving too much equity to AoE weapons.
IN8 - Gives you most conversation options as well as a lot of skill points to outweigh Gifted's™ penalty. Once again for those rare cases you need more Mentats are the way to go.
AG10 - No commentary. Though ranging anything 8 to 10 is flexible with perks so you can somewhat vary points if you want to max out another attribute.
LK7 - LK9 is obtainable via zeta-scan and oh boy am I naughty - I like to become a VC citizen via that test with ridiculously high checks.

Small frame and Gifted™ traits are used. Didn't include the surgery bonuses for final score and from my experience PE7 IN9 is better than PE8, IN8 those are interchangeable imho, your call though. Final thoughts on Small frame: If you have the discipline to properly manage distribution of stuff among party members, yourself and car you should go for it.
 
I've been playing two games in parallel, alternating between these two characters:

Lucky
Female
ST: 5
PE: 10
EN: 2
CH: 4
IN: 10
AG: 6
LK: 10

Gifted, Finesse; Tag Speech, Traps, and Doctor

Warrior
Male
ST: 8
PE: 8
EN: 1
CH: 2
IN: 10
AG: 10
LK: 1

Heavy Handed, Fast Shot; Tag Speech, Doctor, Unarmed

The really low endurance is my latest thing. It adds a real challenge, especially early. Tagging Traps helped Lucky a lot, because of the trap room in the Temple of Trials. Basically I level up that much faster at the beginning. Also, not tagging normal things like Lockpick means that I spend a ton of skill points on that skill. Then, later I pick the Tag! perk and get a truck load of skill points all at once at a time in the game when it's very helpful. And some would say that ST:8 is a waste because of perks and armor, but I dig it. Being able to wail on geckos early on is so satifjying!

I also like playing the two characters/games in tandem because then I get the chance to approach situations differently and compare.
 
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