Fallout: Character Progression

There are two critical aspects to progression in Fallout / Fallout 2 : your character itself (the stats blocks) and his inventory (items). With the minor exception of recruited companions, nothing else will contribute to your overall strength and ability to move forward with the game.

While various builds will have various needs, enabling some niches, there is still a rather clear general progression and ranking for both perks & gear.

For now this page will focus on Fallout 2 perks, because they're essentially Fallout 1 perks with some more added. Do be careful if you're planning a Fallout 1 build.

Perks

Chosen at level-up

Perks are acquired once every 3 levels, or once every 4 levels if you pick the Skilled trait, which you should not. You will only see the available perks when leveling up (which is limited by 3 types of pre-requisites: ability score, skill score, player level), but the complete list is available in the manual. As you're likely playing a digital version nowadays, you may want to refer to the full list of Fallout perks

Those perks will never let you down, and you're likely to pick them for every single playthrough. Alternatively, those are the ones you may want to avoid to increase the challenge. Listed in alphabetical order within the tier.

Action boy, level 12+. Once you have "the" weapon and style you want to use (aimed shot vs many shots vs burst shots), use this to eek out one more action (shooting or reloading) per round if you can.
Awareness (level 3). Lets you see the exact HP, weapon, and ammo level of enemies. Critical to enabling tactical decisions.
Better Critical (level 9). Upgrades every crit into a "better" one, for instance going for instant-kill instead of stun. Applies to every damage type, so both melee & range benefit.
Bonus move (level 6) : similar to action boy but restricted to movement. On the other hand, double value. Lets you peek in from cover, shoot, go back. Or just run away.
Bonus rate of fire (level 6) : Godlike for anyone using any type of gun. Stacks with Fast Shot trait.

And then we have to scroll way down to find anything else useful...

Quick pockets (level 3) : action economy, 2 AP instead of 4 to access inventory. From the inventory screen you can use however many chems and reload (or swap) any gun for free. So good it might be considered cheesing.
Slayer/Sniper (level 24) : Absolute best, with no other perk coming even close. Turn every melee/ranged hit, respectively, in a crit.

In-game action

Many unique perks can be obtained through actions & dialogues here and there, often added minor (but useful) benefits. However, discussing them would be intrinsically meta-gaming.

Gear

Consumables

Survival

Stimpaks are your go-to item for healing. They stack to infinity with no weight and restore 10-20 HP when used. As shops have a very limited amount of cash on hand, buying out every stimpak you can afford is generally possible and wise past the earliest stages of the game. Note that many enemies carries (and use) them, so the faster you kill them the more you can get.
Antidotes can be quite useful in F1, but have pretty much no use in F2, nor can they readily be found there.
Buffout & Mentats are there to pass ability checks you otherwise couldn't. They're high-value weightless items, so you can use them for currency in a pinch.
Psycho's main purpose is turn you into a fairly unstoppable tank for a short bit.
Rad-X and Radaway help fight radiation. The first is preventative (take before going into irradiated area to reduce the effect) and the second curative (take after to purge your system). Quite situational.

Most everything else is situational or flavour-level of power.

Super stimpak

Provides +75 HP (capped by max HP) healing when used, followed by an after-effect of -9 HP. Combat benefits are obvious, but the main use is to overheal NPCs to the point of killing them minutes later. This is an extremely common strategy for challenge or speedruns, but a clear argument can be made for "cheese".

Everyone is welcome to make his own mind and rules.

Explosives

Plastic explosives is a strict improvement over dynamite. Try to keep 1-2 in stock as several quests require one (of either) and it's a viable alternative to opening many doors.

Tools

Lockpicks have a strictly better than previous progression : Nothing -> Lock Picks -> Expanded lock pick set. This is also true for Electronic ones (regular -> Mk II) but they apply to a different set of doors.All of them rely on the matching skill.

"Tool" itself is your generic multi-purpose tool, and generally triggers a Repair check (with bonus).

"Motion sensor" is a fairly rare tool, whose main benefit is providing a +20% bonus to Outdoorsman if help in player's inventory. No real drawback, but largely unnecessary.

Condoms are used automatically when applicable, most notably when "courting" the Bishop ladies. Doing so without one (each time) will trigger a dedicated ending for New Reno, which you may or may not want. No in-game effect though.

Weapons

Do pay attention to the effective range of the weapon. It can be a good idea to keep and alternate between short-range and long-range ones.

Be extremely careful around companions with anything resembling a ranged weapon, especially a burst one.

Almost every small gun is viable and an improvement at the time you get it. Chose depending on playstyle, skill level, ammo scarcity, flavour, and damage types. Also, you're going to be shooting quite a bit so the noise the weapon make can be a deciding factor.

Big guns are few and quite specific : miniguns (ammo guzzlers), flamethrowers (burn baby burn) and rocket launcher (ammo too rare to be viable). Overall the Bozar is the absolute best in the category, having both tremendous damage output and readily available ammo.

Energy guns are excellent options but restricted to mid-to-lategame, as you won't find any at all until New Reno. As a whole, they don't supersed any other type of gun, but offer unique damage type, which may be vastly superior (or not at all) to regular guns.

Throwing isn't a realistic option at all. A notable exception is Pulse grenades, which while very niche do excel in their role. Plasma grenades offer great damage too, but you'll only notice because you're on the receiving end of them when navigating the southern worldmap.

Melee weapons and Unarmed combat should simply be avoided whenever possible for hardcore playthroughs.

Companions

To be clear : if you're coming from most party-based RPG, expect a shock. Fallout 1/2 are designed with solo in mind, and merely have a few companions as a bonus, rather than being designed to be played as a group and solo being the oddity.

This largely translates to the UI and very limited control of said companions. Hardcore playthroughs in particular will have you wanting to run away from a given encounter sooner or later, and your companion(s) will happily keep engaging the enemies while you do so, commonly leading to their death (and loss of their gear). On the other hand, this does give you one-off chance at staying alive.

Fallout 2

Sulik (Klamath) is likely the first companion you'll encounter, but maybe not get. Don't trust his look & desire to fight in melee, he'll die. Give him an SMG and a wide berth. Outside of combat his main benefit is his outdoorsman skill (40% + 10% per his levelups) overriding your own if better.
Cassidy (Vault City) will happily join upon prompting, and is the "vanilla" companion. Level-headed, using regular guns, etc.
Dogmeat (Special Encounter) needs to be put in a safe place, or you'll lose your dog sooner or later.
Goris (Vault 13) joins on request and is a perfect exemple of "extra life companion syndrom". He can't wear armor, only fights in melee, and will tank for you whether you want him to or not, until his fairly guaranteed demise.
K-9, Lenny, Davin, Miria, robodog : extra-lives, if that.
Skynet (best brain), Myron, Vic : somewhat decent options, as they're at least smart enough to avoid melee. Main reason to have them along is their expertise in a field (repair for Vic, etc), as well as the quests involving their recruitement.
Pariah dog : the best tank in the game. But you need to fail a Luck still check to get it, that should be all the red flag you need. Actively try to get rid of him.