There has been some great feedback regarding equipment in RPGs, thanks everyone.
It makes me think that I've been generally on the right track for equipment in Walkabout.
Walkabout is an evolutionary descendent of FUBAR, and FUBAR has never really had an organised equipment system because it's all about freeform chaos, loosely reigned by the choices of the players, the GM and the random draw of objective/location/conspiracy cards. My attempts to apply equipment into the FUBAR system have tempered the chaos, but that's not what FUBAR is about...so every attempt to quantify things has felt wrong. FUBAR has a propensity for gonzo...I want Walkabout to be a bit more low key.
But back to equipment...
A few key ideas spring to mind from my thoughts about roleplaying Vector Theory, these have been informed by various comments in response to my last post.
Equipment as Standard Possessions - This was always going to be the default position for the game; after all, it's the default position of FUBAR. If a character has a "firearms" skill, they have access to a gun. If a character has an "investigation" skill, they have the scientific accoutrements, occult paraphernalia or notebooks necessary to piece together the clues before them. We don't need to worry too much about encumbrance or cost of the items, because this game doesn't aim to simulate a realistic world...it's all about telling the heroic stories of a wandering group aiming to restore the balance in a world struggling back from spiritual chaos.
Since the possession of equipment is the standard state of affairs, the change comes in two ways. Benefits come from the possession of improved equipment or higher quality tools; penalties come in the form of damaged or missing equipment. From a Vector Theory perspective, an improved set of equipment provides a better chance of a beneficial outcome once a decision point is reached, while a diminished set of equipment provides a better chance of a detrimental outcome once a decision point is reached...or it prompts a player to think of a new way to approach a decision point, a way that involves a different skill set and different equipment requirements.
Equipment as Binary Enablers - You need silver to kill a werewolf, otherwise she just regenerates. It's just a fact within the genre. You need an oscilloscope to perform a wave-form analysis, no other tool will do it. You need to have The Ring before you can throw it into the volcanic caldera of Mt Doom.
From a vector theory perspective, there might be certain blockages to the passage of a story. Such blockages simply prevent further passage unless specific items are possessed or specific new paths are found. This leads back to the traditionalist styles of game play, where a specific scenario is written, specific pieces of equipment are found along the way, and each of these unlock a new part of the scenario until the final goal is reached. It's also the way most computer RPGs work...do you have it? Yes, proceed. No, go back and do the level again.
Don't get me wrong, I think that binary enablers are a great feature of story, if used correctly and not over-used. The possession of a binary enabler often allows a character to bypass the mundane ("I have access to a Stargate, so I don't need to travel for years to get from world to world...I can just step there"), this allows us to get into the meat of the story. They also provide situations where players simply can't do things that might derail the game because they don't possess world shattering items.
If we don't want invisible characters, we don't provide them with invisibility suits...they can try to be a stealthy as they want, but true invisibility is out of the question...and that's where a lot of games go haywire.
Equipment as a resource - In games where there is a huge equipment list, many of the items available have little benefit as tools. Some are simply more valuable than others because they are rarer, not because they are better. Most versions of D&D capitalise on this by including "treasures" in the form of artworks and antiquities, you can't do anything with them, but there are people back home who will pay good money for something pretty. In a post apocalyptic setting, this is less of an issue because items tend to be valued more for their ability to overcome issues in the world rather than their simple aesthetics or degree of exoticness...but it still plays a minor factor because the possession of something unusual might provide a benefit in the form of prestige. ("I have an Italian porcelain statue that is four hundred years old...no it doesn't do anything, and it's very fragile, but that just shows how much power I have...I can protect something as delicate and beautiful as this").
If a piece of equipment is worthy of being written onto a character sheet or an index card, it should have a quantifiable impact on the story and the game. Vincent Baker's "Clouds and Boxes" could be linked here, with the theory that if something is in the story it should be reflected in the game mechanisms, and if something has an impact on the game mechanisms then it should have narrative implications in the story. How you value an item depends on how much it impacts on the story (Does it provide a skill bonus? Does it open up a new part of the story? Can it be used to trade for favours or other advantages?).
Equipment within the Walkabout Rules - With this in mind, Walkabout will assume certain possessions within it's game mechanisms. Characters will start with a basic list of flavour items, such as the type of clothes they wear, and the equipment common to their people (some of these items might have a bonus or penalty associated with them). Most of the characters will be limited to carrying the possessions that actually help them in their journey, superfluous items will need to have value as trade goods otherwise they simply aren't worth carrying around. No matter the item, it will have value.
Using the genre conventions of the post apocalypse, it also makes sense that pieces of equipment are frequently in need of repair...and those items used most often are typically the most patched up and jury rigged items a character will posses. You can keep an item pristine, or you can try to gain advantage from it in exchange for risking damage to it. You could always sacrifice the item completely to gain an even better advantage.
I'll apply this to some specific situations.
A sword - A character with a melee skill might automatically possess one of these, a character without the melee skill might pick one up (they won't be proficient in it's use but it still provides a bit of an advantage).
The character without the melee skill can gain an advantage from the sword, but they risk damaging the sword because they don't know how to use it properly (+1 but risk of damaging sword).
The character with the melee skill can justify using their melee skill simply by virtue of possessing the sword, no advantage is gained or lost and no risk is taken with the sword (+1 from flat melee skill).
The character with the melee skill can push their luck by combining the benefits of their skill with the benefits of their sword. This combines the bonus, but risks the sword (+2, but risk of damaging the sword).
Once the sword is damaged, it gains a negative "damaged" trait. This doesn't offset the sword's inherent bonus, but the next time the sword is "damaged" it becomes irreparably broken if used before it is adequately repaired (the damage trait is bought off with a successful "repair" action).
The flip side of damaged items comes in the form of those which are well maintained (or of good quality). A sword might have a bonus trait associated with it (+Sharp, +Dangerous, +Poisoned), where this bonus might be applicable to a situation and a character can justify their proficiency in using the item, an additional bonus is applied. The trained user might get a double bonus (+1 from the melee skill, +1 from the bonus trait attached to the sword, and a possible +1 if the are willing to risk damaging the item). The untrained user still only gains the single level of bonus if they are willing to risk the item (The simply don't have the knowledge to activate the attached bonus traits).
A trained character can sacrifice the bonus traits associated with an item, or may deliberately add a damaged status to an item, in exchange for a guaranteed additional level of success...not a bonus which might increase success chances, but a definitive success. A "+Poisoned" sword might translate to an automatic additional degree of damage if the bonus trait is sacrificed, or it might be used carefully as a series of ongoing bonuses that don't permanently sacrifice the trait (but which risk the trait every time it is used).
This makes a character's skills more important to them, but items become a catalyst to push characters to far more powerful levels.
Clothes - Most clothes provide no specific benefit or penalty, they simply are. Some clothes might have specific benefits associated with them, they might be "+Fashionable", "+Armoured" or "+ Camouflaged". These traits may justify the use of specific skills during the curse of play, or they may be used to provide bonuses at the risk of losing such traits. Clothes may have negative traits associated with them as well, such as "-Fragile" or "-Dirty", these traits won't necessarily apply to all situations but the could come into play. A "-Fragile" set of clothes would be instantly destroyed rather than dropping to a "Damaged" state, while a "-Dirty" set of clothes wouldn't provide much benefit when trying to impress someone with the Deportment skill.
I think this has a nice balance between storytelling through the items, mechanisms for gameplay, and simulation of the post apocalyptic genre. It's not the perfect set up for every game or every story, but the systems are starting to crystallise in a pattern...things seem to be falling into place.