Title says it all, what special choice is the best no matter what playthrough you are playing. I'd say luck as it affects crit, enemy mishaps and gambling.

Intelligence since it allows you to get the most out of your skill points which are vital to get as much of in this game, along with allowing you to pass many skill checks and giving you boosts to important skills like Science and Medicine.

No Endurance. No implants.

Intelligence, because it affects how many skill points you can have.

Luck!

Intelligence is so much more important than the rest it's not even funny, they really need to decouple it from SP gain per level. The eventual L50 cap will change that, though, unless one is trying to cap everything.

I would consider Strength fairly important as well, since without it you cannot carry stuff nor use most weapons properly.

Intelligence is not that important since you can get Educated with 4, which is equal to 4 points of Intelligence.

Endurance is pretty important, but there are very little reasons to have more than 7 implants. On the other hand, there are very little reasons not to bring Luck to 10.

I love the myth that a high Intelligence matters. It was a myth in FO3 as well.

My character will max all skills at 100 with only 6 starting Intelligence at level 48-49.

Agility and intelligence.

STR - Not that important. With an implant, power armour and Weapon Handling you only need 5 STR to use any weapon.
PER - Not that important. 6 for that important perk.
END - Not that important. Implants are nice but you don't need them. Unless you're careless and overly gung-ho 4-5 should give you enough health.
CHA - Depends how important companions are to you.
INT - Not that important. 4 plus educated gives you enough skill points, especially with Comprehension and collecting certain skill magazines whenever you see them.
AGI - Quite important. Want as much as possible.
LUC - Very important. Want as much as possible.

Of course that all is dependent on playstyle, RP limitations placed on self (my Cowboy wasn't educated so needed more INT, wouldn't be seen dead in power armour etc), how much you use VATS or want crits (a lot being my answer to both) but it works for me.