What are some essential, or otherwise excellent, stats and perks for non-melee players? Also, is there any way to affect which perks are available to you at level-up?
A lot of them have a min level, just flip trough them so see which one are marked as "new" each level up. Don't level up perks until you are max level, the base version is enough. Action boy is the exception. Concentrated fire is necessary to target limbs, otherwise you can't do much wrong picking perks. Once you are level 50 you can pick a new one or shuffle stat points around each level up anyway, don't worry.
The weight reducing perks are.. more of a "I didn't have anything else to pick" thing until you know what you want to focus on. If you are going for chems, you obviously need TP. I picked bear arms and bandolier because 'dexi hauls more ammo and weapons around than the army of Lichtenstein.
And yeah, backpack. Normal one gives... 60(?) and the turdpole backpack with high capacity mod gives a total of +120 carrying capacity.
Also deep pockets in your armor for +10 per piece.
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A general PSA:
Choosing what SPESHUL stat to increase and chosing the perk card are TWO DIFFERENT THINGS! The game does not tell you that, you can pick a card from a different stat by filtering them differently. Codexia was originally very brainy because I picked all the hacking perks early.
If you want to switch between PA and sneak, you need a decent amount of STR tho, but I assume you want to go for the standard sneaky sniper.
Weapons:
You want a silenced weapon. Sneaking is the way to go and sneak attacks get so many extra dmg. If they don't bug out, as they currently do a lot.
All the cool kids seem to go for the handmade for automatic fire or lever action for single shot.
Pistols are... not good for "endgame" use. The high dmg ones are revolvers, so no silencers, also no armor piercing perk for pistols. You CAN make it work with a good legendary. E.G. I have a lvl 40 instigating vats crit western revolver I wanted to discard, but boy that thing deals 1000+ dmg on a stealth headshot.
Shotguns got nerfed a while ago, and are horribly buggy right now, you can't hit shit outside VATS and with it you HEAL enemies half of the time, thanks to stack overflow. They have great utility tho, used with the enforcer perk you can really cheese fights, since the cripple chance counts per PELLET. So each shot pretty much cripples the leg or wing. An immobile bear is no danger anymore.
SPECIAL:
CHA: (4) Lone Wanderer. Duh.
PER: (15) 9 are reserved for the maxed rifleman/archer/commando, 3 for concentrated fire, 3 for tank killer/the bow AP perk
AGI: (15) 3 each for Action Boi, Sneak and Covert Operative. Escape Artist is great. Fill the rest as you like. I don't like dodgy, it steals to many action points.
LUCK: (at least 11) 3 for Class Freak + 2 for Starched Genes (mutations) and 3 each for Grim Reaper and Four Leaf Clover. Serendipity super awsome if you go for bloodied, but I would just trade FLC for it in that case. Does not work in PA btw.
You can of course go lower if you like, especially if you go bloodied. Since unyielding armor will end up putting your SPESHUL up to 30 (except END) and you only went 15 PER/AGI for 2hit chance and action points, you can lower some AGI/PER if you need them elsewhere. I for example ditched tank killer, since I kinda sorta think sneak attacks bypass armor anyway? You deal enough dmg anyways.
But that's finetuning you do beyond level 50.