Which stats/perks are more important in new survival mode?

Around level 19 now. Here are a few I've found helpful:

Lone Wanderer - invaluable, especially with the carry capacity boost.

Ninja - I'm sticking with a sniper/stealth build, so it's helpful to cause max damage from as far away as possible.

Gunslinger - due to many factors, it's harder to gather junk, and since pistols are easier to upgrade at lower ranks for Gun Nut, I started with Gunslinger instead of Rifleman. Will add that later.

Local Leader - you'll want to get this going as soon as you can. Once you are out in the wild, it's very helpful to have access to all of your workstations, especially with no fast travel and limited carry capacity.

Demolition - explosives have been very important for me thus far, and making them more powerful and having the ability to craft them, is even better.

Oddly enough, I don't think I've taken any of the first 8 perks listed above. Started with STR 1 and END 2. Just a different playing style.

I have a lot of playtime on Fallout 4. This includes beating the original survival difficulty in less than 6 hours of game time, below level 20.

I'm now nearly level 30 in the new survival mode, taking my time. I'm on my way to the Glowing Sea.

So far, I haven't had to change my play style barely at all. The combat is essentially the same. The best way to survive is still to kill everything in VATS before it gets to attack you. The extra damage actually makes this easier. But, it also makes the whole killing them before they attack that much more important. So, continue to focus on doing spike damage with crits, and using Awareness to ensure that the damage from each shot matches the target.

This means that the most important SPECIAL stats continue to be Perception (accuracy), Agility (AP), and Luck (crits). My character has 2 Strength and Endurance, and no perks from either of those columns.

The only real differences I've found that affect my perks are the need to carry around additional supplies in the form of food and water, and the inability to fast travel back to my main settlement. This means that you need more carry weight, and more access to crafting supplies and stations. Therefore, Local Leader is the perk that has had its importance increase the most.

You need supply lines to your forward settlements so you can

• sleep (save)
• heal your radiation (http://fallout.wikia.com/wiki/Decontamination_arch)
• cook food
• drop off junk without running all the way back to your main settlement

Also, Local Leader is required to build stores in your settlements. This means you won't have to run for ten minutes just to sell your loot.

Due to the carry weight issues, you might consider Strong Back or Lone Wanderer, but there are other ways to address this issue beside wasting perks on it. You can use pocketed or lightweight gear, be more judicious about what you pick up, and take advantage of a companion. See this other answer for more info on increasing carry weight.

For survival, because of weight limitation, I decided to go with gunslinger and all the critical hits perks (ninja, better criticals, critical banker...)

The goal is to kill before being killed.

Most of my early build is based on "Many a True Nerd" (https://www.youtube.com/user/ManyATrueNerd) Survival Build; I am not certain to follow his build later on in the game, but it is a good start.

One of the keys is adaptability. Change your thinking a bit and focus on survival. Commando perk is OP IMO, works on anything you can make automatic fire - laser guns, rifles, pistols. You get three shots for every pull in VATS and dealing damage is what you want. Pick a favorite weapon and shoot. Laser guns are great (not what I am using) because you just use fusion cells and can sell every other bit of ammo. Scrounger perk for finding the ammo and Strong Back and Lone Wanderer for carrying everything.

Here is my current build, at level 21 now, totally OP with the Overseer's Guardian (purchased from Vault 81) in Survival Mode:
S-6
P-5 (bobblehead from Concord/Minuteman quest)
E-5
C-3
I-3
A-5
L-3

Level ups:

2-Scrounger
3-Locksmith
4-GunNut
5-Commando
6-Lone Wanderer
7-Scrounger rank-2
8-Bloody Mess
9-Bloody Mess rank-2
10-Life Giver
11-Commando rank-2
12-Armorer
13-GunNut rank-2
14-Armorer rank-2
15-Life Giver rank-2
16-Strong Back
17-Lone Wanderer rank-2
18-Strong Back rank-2
19-Locksmith rank-2
20-Life Giver rank-3
21-Commando rank-3

Total carry-weight is ~270 lbs which is really nice. The only downside so far is you have to find/buy Antibiotics (which seem to be more rare than the other medical items (stimpaks, radaway, etc.) but so far so good.

I'm going to go ahead and assume you know how to play the game. Finding the balance between combat perks and others that suits you. Being willing to reload and grind a bit etc.

So: infection. There's lots of hassles in survival mode but they are just hassles. Infection takes a chunk out of your heath pretty regularly. You need antibiotics or a doctor. Doctors are rare. So get the Chemistry perk and make some. You still have to find the components but it's not that hard, just go on scaver runs and look out for glowing fungus.

As a bonus: psychojet: you can win most fights with the judicious use of this and a decent rate of fire. Also Refreshing Beverage cures addictions.

That's my advice. Also remember: huge endurance does not guard against infection. Also check the bathroom mirror cabinets in Sanctuary for antibiotics, and don't waste it on illnesses that really don't matter.

Ignore all resistance perks. Even wearing full power armor, you still go down after 2 hits from the emperor radscorpion. This meager resistance really isn't going to make a difference.

Invest in damage from non-automatic rifles, damage from sneak, sniper perk, later on, in party girl (you use chems a LOT, but it's fun to actually have to deal with the addiction for once in Bethesda Fallouts, instead of just teleporting to a doctor)

Improved carry capacity as well.

Sneak of course.

With this build, you can oneshot Alpha Deathclaws. The biggest threats are molerats, ghouls and in general, any swarming enemy.

With few exceptions, 2 sneak shots and several more while the enemy is charging at you, should be enough to kill them, if you use psychobuff + jet.

As you mentioned, playstyle does have a lot to do with it. I did see a lot of potential in the endurance perks, but I passed since I wanted an int based character to explore all the modifications to weapons and armor. I stayed at one endurance until level 40.

Sprinting- So yeah, you can't fast travel in survival. I eventually realized that I should find a way to minimize my manual travel time and I did it with the following.

Base SPECIAL: Endurance for longer sprint times, Agility for more AP.

Moving Target, (rank 3): Reduces AP spending on sprint.

Action Boy/Girl: Faster AP regen.

Science!, (rank 3): Built the power armor leg mod for higher AP spent on sprinting but you go faster (overdrive servos).

Chemist: Jet fuel. If you get your charisma up (or have good charisma gear) and make grape mentats when you can, buying out vendors of flamer fuel and fertilizer to make Jet Fuel not only helps you get to places quickly, but it sells for quite a bit. Being in need of caps is kind of an abstract concept when you're a drug dealer.

Nuclear physicist; Scrounger (if you're sporting power armor): You'll get more out of your cores and you'll find more of them with scrounger. If you go without power armor, I'd suggest two leg pieces with 10% faster run speed.

Other mentions- Scrapper: Some of the advanced guns and armor give you a slew of raw materials. When in an area with a weapon or armor station, you can loot everything you can and break it down to carry back.

Strong back: Wasn't happy with rank three. The first two are good.

Note on Endurance: At 96 I still only have three endurance (and three life giver). This appears to be plenty for reducing sprint AP considering the other perks I've invested in. More couldn't hurt, though, and the perks are good.