I'm currently on Chapter 9 on the airship, but that's not too important right now. The problem is, I am flat broke, and I don't know what to do. I've noticed that the weapons I've picked up along the whole game can be sold for a good amount of money. But I'm not sure if these weapons will become incredibly useful later in the game, once you upgrade them. 
 
So I need the helpful advice from those who are farther in the game or have finished. 
 
Currently equipped are:
Bladed Lance lv. 6 (Fang)
Power Circle lv. 2 (Snow)
Gladius lv. 7 (Light)
Binding Rod lv. 4 (Vanille)
Airwing lv. 3 (Hope)
Procyons lv. 2 (Sazh) 
 
Now what I have in my inventory are:
Vidofnir lv. 1 (Hope)
Gae Bolg lv. 1 (Fang)
Axis Blade lv. 1 (Light)
Spica Defenders lv. 1 (Sazh)
Healer's Staff lv. 1 (Vanille)
Lifesaber lv. 1 (Light)
 
Now some of these are made for specific paradigms, which is why I kept them, but are any of these worth upgrading or are they vendor trash?

I can't really speak for any weapon specifically. I just upgraded my initial weapons and never bothered with any other else and had no problems in any battles. I just didn't seem to make sense to me to start upgrading another weapon when one of them was already so developed. Sure, you could probably be more effective if you use them more tatically, but I think you can stick to whatever you feel is best and have no problems beating the game.

If you're going for Treasure Hunter, you should be keeping them, so you can upgrade each of them to second-tier.

I recommend Hope's Hawkeye weapon, if you can buy it. You should have gotten it along the way though.

Don't upgrade anything yet it cost's way too much money. Also don't sell the weapons yet either. I would hold onto the weapons until you decide which ones you want to upgrade. There is an art to the upgrading process as it is very expensive and very detailed as how to actually do the upgrades. I'm currently power leveling before the final boss and I'm using Lightning with The Blazefire Sabre (I upgraded it to its 2nd form) Snow with Power Circle (upgraded to second form) and Hope with the upgraded Hawkeye (2nd form).
 
You should wait until Chapter 11 or 12 to even start upgrading the weapons and even then you won't have enough money to get it to it's 2nd form (each weapon has 3 forms). The weapons each character starts with are balanced in Strength and Magic, Others are higher in one and low in the other, others are low but have special status effects. I have the guide so if you have specific questions I'll help, but don't worry about that until chapter 11 or 12 as it takes alot of grinding and $.

If you want to get Fang's theme/the Treasure Hunter trophy, then I'd save all the weapons you get.  If you don't care about that and just want to beat the game, stick with one weapon per character. 
 
Basically if you want that trophy, you'll have to upgrade every weapon (there's 8 per character) to tier '2' (where the name changes.  For example the Blazefire Saber becomes the Flamberge at tier 2).  You'll have to upgrade ONE tier 2 weapon per character to tier 3.  

I'm pretty close to finishing the game, and have upgraded a couple of weapons to their second stage. 
 
Based on the stats and how I use my characters, here are what I feel are the best weapons for everyone : 
 
 gladius - lightning 
spica defenders - sazh 
power circle - snow 
hawkeye - hope
belladonna wand - vanille 
dragoon lance / pandoran spear - fang 
 
the reason I list two for fang is because I don't think you can get her best weapon until after you finish the game, which seems a bit useless imo. Nevertheless, dragoon lance has the best stats of all her weapons. Sell any weapons that aren't the one's I've listed, and focus on upgrading equipment (the ones that raise magic and strength are most useful up to chapter 11)  
Once you get to chapter 11 you can start collecting items and cp and start doing some proper farming.  
 
There's a good guide here:  http://www.gamefaqs.com/console/ps3/file/928790/59331 
and here:  http://www.gamefaqs.com/console/ps3/file/928790/59442

I went with the Axis Blade -> Enkindler for Lightning because it contributes to the Boost synthesis ability, which speeds up your ATB recharge by 5% per item. With the Enkindler and two other Boost items (I had Sprint Shoes and Aurora Scarf on her), I had all these effects for her in total: 
  

• +15% to ATB recharge 
• First strike (begin battle with ATB gauge filled) 
• Slightly recharge ATB on every hit
• Auto-haste  in every battle  

Brad, dude. You're such a nerd. 
 
I'm still waiting for my copy to arrive. Hopefully it'll get here shortly after Easter. My fingers are itching.

Man that weapons stuff is so unecessarily obscure and complicated. I hate having to look at guides for games, but this is the first I've heard of synthesis and I'm at chapter 11. And if I'm missing out on bonuses like auto-haste I guess I'll have to trawl the faqs. Annoying
 
Edit: @Brad: How did you get the auto haste? It isn't under the boost synthesis ability.

" Man that weapons stuff is so unecessarily obscure and complicated. I hate having to look at guides for games, but this is the first I've heard of synthesis and I'm at chapter 11. And if I'm missing out on bonuses like auto-haste I guess I'll have to trawl the faqs. Annoying  Edit: @Brad: How did you get the auto haste? It isn't under the boost synthesis ability. "

" @ClownDetective said:

" Man that weapons stuff is so unecessarily obscure and complicated. I hate having to look at guides for games, but this is the first I've heard of synthesis and I'm at chapter 11. And if I'm missing out on bonuses like auto-haste I guess I'll have to trawl the faqs. Annoying  Edit: @Brad: How did you get the auto haste? It isn't under the boost synthesis ability. "

The first 10 chapters of this game was a big tutorial, they explained everything to the point that I just didn't pay attention anymore.     BTW; the auto haste thing comes from an accessory you equip. Most people synth/upgrade/dismantle some other accessory to get this one, and its not auto haste, its start battle with haste. If the battle goes on for too long the effect wears off and you got to actually have someone with that spell to rebuff them. Still a good accessory but not as good as auto haste would have been.  "

" @ClownDetective: Exactly as it sounds, Sprint shoes. I love the paradigm system in the game, but having played a crap load of JRPGs including Demon souls, I've become accustomed to learning fast in videogames by learning the importance of things in 3 minutes instead of 3 hrs to pound in my head things like use sentinal. Interrupting and staggering them are two different things (one is commando the other is ravager), usually people have a paradigm with both, but honestly when you can switch things out so easily I'd say use two paradigms going all out stagger or interrupt and just switch between the two manually.  "

" @ClownDetective said:

" Man that weapons stuff is so unecessarily obscure and complicated. I hate having to look at guides for games, but this is the first I've heard of synthesis and I'm at chapter 11. And if I'm missing out on bonuses like auto-haste I guess I'll have to trawl the faqs. Annoying  Edit: @Brad: How did you get the auto haste? It isn't under the boost synthesis ability. "

The first 10 chapters of this game was a big tutorial, they explained everything to the point that I just didn't pay attention anymore.     BTW; the auto haste thing comes from an accessory you equip. Most people synth/upgrade/dismantle some other accessory to get this one, and its not auto haste, its start battle with haste. If the battle goes on for too long the effect wears off and you got to actually have someone with that spell to rebuff them. Still a good accessory but not as good as auto haste would have been.  "

" @StaticFalconar said:

" @ClownDetective said:

" Man that weapons stuff is so unecessarily obscure and complicated. I hate having to look at guides for games, but this is the first I've heard of synthesis and I'm at chapter 11. And if I'm missing out on bonuses like auto-haste I guess I'll have to trawl the faqs. Annoying  Edit: @Brad: How did you get the auto haste? It isn't under the boost synthesis ability. "

The first 10 chapters of this game was a big tutorial, they explained everything to the point that I just didn't pay attention anymore.     BTW; the auto haste thing comes from an accessory you equip. Most people synth/upgrade/dismantle some other accessory to get this one, and its not auto haste, its start battle with haste. If the battle goes on for too long the effect wears off and you got to actually have someone with that spell to rebuff them. Still a good accessory but not as good as auto haste would have been.  "

 The Synthesis stuff is really poorly documented, so yeah, I had to look it up online to tweak my characters that thoroughly. That's a big knock against the game in my book. (Maybe I should write that review now.)

" @ClownDetective: That's an interesting comparison which I frankly don't agree with. Metriod was still fun even with gimped equipment since I am involved in the jumping and shooting. FF13 on the other hand, once you find out you have to use a certain class to get through these enemies (say sent, or whatever), I'm just pressing X over and over again. At least in past FF (or any RPG much less JRPG) I was more involved in the game by having to micro my guys (yes it is also pressing X over and over, but the involvement is the choice I'm making).  
 
 
@Fallen189: I love FF and I respect them for doing the paradigm thing which was a big gamble, but honestly the game is far from perfect but also in no way a bad game as well. Like any other big name game out there, there will always be people that love it and others that hate it. The only big difference is FF13 will actually get the scores is deserves as opposed to over hyped games just because the whole JRPG (even though FF13 plays nothing like a traditional JRPG) genre isn't mainstream popular.  "

" @ClownDetective: That's an interesting comparison which I frankly don't agree with. Metriod was still fun even with gimped equipment since I am involved in the jumping and shooting. FF13 on the other hand, once you find out you have to use a certain class to get through these enemies (say sent, or whatever), I'm just pressing X over and over again. At least in past FF (or any RPG much less JRPG) I was more involved in the game by having to micro my guys (yes it is also pressing X over and over, but the involvement is the choice I'm making).  
 

" @StaticFalconar said:

" @ClownDetective: That's an interesting comparison which I frankly don't agree with. Metriod was still fun even with gimped equipment since I am involved in the jumping and shooting. FF13 on the other hand, once you find out you have to use a certain class to get through these enemies (say sent, or whatever), I'm just pressing X over and over again. At least in past FF (or any RPG much less JRPG) I was more involved in the game by having to micro my guys (yes it is also pressing X over and over, but the involvement is the choice I'm making).  
 
 
@Fallen189: I love FF and I respect them for doing the paradigm thing which was a big gamble, but honestly the game is far from perfect but also in no way a bad game as well. Like any other big name game out there, there will always be people that love it and others that hate it. The only big difference is FF13 will actually get the scores is deserves as opposed to over hyped games just because the whole JRPG (even though FF13 plays nothing like a traditional JRPG) genre isn't mainstream popular.  "

I like it, but the difficulty spikes get so insane sometimes. I just hit the end boss of Chapter 11, and it's destroying me. Some bosses are just fucking insane :( "

" @Fallen189: I dunno, I had trouble with a couple of bosses (both in chapter 11) but I managed to get them after a few tries being under-leveled and under-geared. I don't think there is a single boss in the main story I would call fucking insane. Maybe it's because I play a shit ton of RPGs (some of which have been pretty brutal), I dunno, but I thought the difficulty curve was excellent through-out the game.  "