Quick question, should I bother upgrading weapons at this stage? I'd personally want to max the hell out of each and every weapon/accessory I get but the components I have are pretty low and I'm not really sure which ones I'd want to upgrade.
We're talking FFXIII, right?

Components with a screw icon (normally have mechanical names) also give a negative to the bonus experience (lowest bonus is x1, there's no worries dropping lower than bonus x1). In return, they can give really big experience points.
Note: Other component icon types may also have negative bonus effects, not just screw icon ones.
I don't think there are any components that are
super rare. Just a few particular catalysts (components with a crystal icon), that are a little harder to get, because they are used to evolve certain maxed items. You won't need to worry about these till you start using these on maxed items.
Most of the time I 'd first use other components to raise the bonus to x3 (like buying a bunch of Iron Shells, around 35, from Creature Comforts).
Check which screw type component gives the most experience.
Then use the "screw type component x all" (all of that 1 component. e.g. Superconductor x13) to push the total experience with the x3 bonus.
The bonus will drop back down to x1 after that though. so rinse and repeat.
There's really no need to hold onto components that give experience, since you'll surely get/buy better components along the way.
Most importantly
REMEMBER to sell all components that say they can be
sold for a premium (e.g. Credit Chip, Gold Nugget, Cactuar Doll). They only give 1-2exp, but sell for a load of cash.
Personally, I upgraded weapons and HP/Magic+ accessories first.