All i've got to say now is that after 10 hours of playing i'm getting rather desperate for something to do other than get into fights and watch cutscenes =P
So when the opportunity first occurred to play with the item upgrade system, i dragged my monitor and keyboard over to the living room table (first time i've done that in this apartment, of course we've only had the living room table set up for about a week =) and got to work playing with some spreadsheets :)
If you want a brief tutorial on the item upgrade system and don't want to read a FAQ, here it is:
(And technically there are spoilers here, if you really care about how many different weapons the characters will eventually get access to. I sure don't.)
The basic system is that items have levels just like the characters used to in older FF games. In the upgrade system you can "spend" the "Component" items you've collected to upgrade either weapons or accessories. Each component is worth a certain number of experience points.
Each upgradeable item requires a certain number of experience points to advance to the next level. Of course the amount of experience needed increases as you increase the level. At some point you hit a level cap, in which case you use a different kind of component (that you can't spend just for experience) to advance it to the next stage. It will lose a lot of levels in the process, and you can start leveling it up again in the new stage.
The first tip you should know, although it becomes obvious very quickly, is that upgrading accessories is rather pointless at this stage. I tried upgrading an Iron Bangle, and it got HP bonuses. It maxed out at level 5 or so, and i used a stage advance item (the only one i have) to advance it to the next stage, and it turned into a Silver Bangle. Just like you can buy in the store. It had a few more HP then your standard store-bought bangle, and of course i could have leveled it up some more, but it's just not worth the time, effort and components that you could be spending on something a lot more effective.
Like weapons. Since i was interested in a single topic, i managed to take a look at some FAQs and _not_ start reading up about everything. It seems that there are about 8 different weapons for each character. Each of those weapons has three different stages, and i think you only ever acquire the first stage weapons. That means you don't need to worry about upgrading your weapon into something it turns out you could have just bought in the next shop. Every weapon's third stage has the same name and is an "Ultimate Weapon." So every character actually has 8 ultimate weapons they can get. If you're willing to grind that much that is.
As is often the case in FF, the weapons are balanced in different ways. There are weapons with lower stats that give you useful status effects, and weapons with outrageous stats that have no status bonus, or even a status penalty.
Definitely some weapons will appeal to some people more than others, however it looks like maxing out a weapons first stage generally costs a few tens of thousands of experience, maxing out the second stage costs a few hundreds of thousands of experience, and maxing out the final stage costs a million or more experience. So there's no reason not to start upgrading a few weapons now even if they're not what you think you'll want for your Ultimate Weapon (assuming you don't intend to max out more than one for each character anyways of course =)
Now for the leveling itself.
I plugged in the sale prices and experience values of all the components i had, as well as the purchase prices of the components in the store. It seems that on a pure cost per experience basis, the best component to buy for leveling is "Polymer Emulsion.
So far none of the components i've obtained can be "traded in" for Polymer Emulsion for an XP profit except for (unsurprisingly) Credit Chips, which are worth the usual "you really don't want to do this" XP value of 1.
There's one other element to spending components to gain experience for your items. Some components provide a bonus to experience gained for the item you use them on. Other components reduce your bonus.
At first i was expecting some kind of "this component provides bonuses for this kind of item" system, but it seems that things are even simpler than that. You seem to collect a lot of items from monsters in pairs, "Begrimed Claw" and "Bestial Claw," "Shattered Bone" and "Sturdy Bone," etc. So far all of these items (Claw, Bone, Fang, Leather/Hide, Fluid and Tears) seem to provide bonuses. It seems like each one has some kind of "bonus" score which adds up with each item spent. Once you spend enough items you'll get a message saying the bonus has gone up. The sequence is 1x, 1.25x, 1.5x, 1.75x, 2x, and then straight to 3x. Unsurprisingly each stage seems to require more bonus points than the previous one.
3x seems to be as high as the bonuses go, or at least, this being FF13, that seems to be as high as they can go for now.
All the other components seem to have a negative bonus score. Not too surprisingly those are the components that give you large amounts of XP. So leveling up items efficiently is a balancing act. You need to spend the "common" components first to get the bonus level up, and then spend the big components with that big bonus, which will lower it back down again. Note that you get a message when the bonus level goes up but _not_ when it goes back down! Always double-check before spending a big pile of high value components!
Also, it seems that although the bonus level caps at 3x, you can keep on adding bonus points on top of that using common components, which means that you can spend a lot of common components and then not have to worry about it dropping back down. However it's also important to note that there are no bonus levels below 1x, and the bonus points don't seem to go below zero. You can spend a large number of high value components and still raise the bonus level back up with just a few common components.
So i don't know what the relative levels of scarcity will be, but in theory the most efficient way to handle upgrades is to save up a large pile of high value components, ideally of just one type. Spend just enough common components to bump the bonus level up to 3x, and then spend the entire stack rare components, repeating the process if you have to spend more than one stack of rare components to achieve what you want.
Be careful though, you can easily spend more experience than is needed for the next level, and the item will jump up more than one level because of it. However you only ever see what is needed for the very next level, and if you're near the level cap i suspect it will let you overspend. So if you want to spend large chunks either check a FAQ to get an idea of what the max level/experience is for that stage, be prepared to reset if you go over it by a lot, or be willing to accept a potentially large loss of components.
A very brief amount of experimentation seems to indicate that it's not worth Dismantling items you've already Upgraded. You can get some useful items from Dismantling unupgraded items (Fortisol and Aegisol) and some components i haven't seen before (Gummy Oil and Transformer) but nothing that seems worth going out of your way for so far.
Edit: Oh, i should also mention that between Lightning's two weapons at this point (Blazefire Sabre and Gladius) the cheaper experience for the Saber beats out the higher starting strength of the Gladius, at least in the medium term. Once you get to about 4000 total experience spent, the Saber has a Strength score very close to that of the Gladius, and a Magic score that far exceeds it. I have no idea if the same pattern carries over to other characters' weapons, but it's probably worth testing out before you commit to one or the other.
(Checking a FAQ seems to indicate that the Saber will max out at 115 Strength/Magic for the first stage. The Gladius will eventually hit 175 Strength and 88 Magic, but you have to spend twice as much experience to max it out as you do for the Saber.)