What @Jefe said, with a side of looking at the guide @Piemanlee posted. 
Resetting can have other consequences. For example, the Grog Nozzle is a mission item, in order to have one you would need to keep the mission open. If you reset you will lose any mission items you might be carrying until you accept the mission again.
Another farmable tied to a mission: the KerBlaster, which you can farm Midgemong for after the Symbiosis sidequest in Blackburn cove.
Okay. So, with the guide I should save the outstanding and good guns for until I’m level 50 and do the rest of the missions that reward average or bad unique weapons to level up to 50 right?
Okay cool I just finished that mission. Is the weapon worth farming? And how are you able to get the best weapon variant of the Fibber if you can only do the mission once?
Within reason. You don’t want to be more than level 52 when you start UVHM, and it would be easy to be higher than that if you tried for every piece of gear you want at 50. That list will help you decide which things are more important for you. An example might be the Teapot pistol. I like it, but you can get a Hornet (which is generally better) from the first boss in the game, which makes having a level 50 version kind of unnecessary. But, if you get it when you’re in Tundra Express the first time it can help with the Wilhelm fight.
I don’t know if I would consider the Kerblaster a great fit for Gaige, but my Axton and Krieg both carry them. As for the Fibber, you can dashboard farm by exiting to the menu if the reward is not what you want. The options are more varied on PC, but I’m not well versed in PC. There are even ways to get multiples, but I’ve never bothered trying that.
Any gun you get in TVHM ( up to level 50 ) is going to get quickly underleveled once you start UVHM. I recommend getting a level 50 slag Fibber or a Slagga - but that’s about it. Worry about mission rewards when you get to 72.
One more thing I have a question about. I know that this is a little off topic of what this thread is supposed to be about, but what are weapon parts? I know that they change the performance of the gun, but how do you know what type they are if the aren’t listed? Type meaning like Hyperion, Jakob’s etc.
Here’s a great guide ( this is probably the 500th time I’ve posted this 
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Thanks for the link. You won’t believe how much that helps me.
It is easily the 500th time @Jefe has posted that. 
A note on quest rewards to save: I like to save the Deadly Bloom (the Overlooked: this is a test reward) and the Love Thumper (Best Mother’s Day Ever reward) for max level with my Gaige. With SiC those shields help DT put out more damage when he’s in play. Also the Flame of the Firehawk is a good one to save if you haven’t done the Cult Following missions yet, but I didn’t wait in TVHM because I wanted the exp.
Oh trust me I know 
I still use it frequently after all this time.
Slag Fibber, huh? Does the barrel type matter in that case?
Asking for a friend. (And again, that ‘friend’ is me. 
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The ricochet barrel makes it Gaige’s premier gun. Because of the post-bounce split, all pellets get full damage instead of Close Enough’s 50% nerf.
I say slag for level 50 because it stays useful for longer than other elements.
How do you know which barrel you got?
For that you’ll just have to resort to the classic trial and error method: shoot and see. Make sure you’re near a wall and shoot at the ground.
But then you can’t get a different barrel of the one you get isn’t the one you wanted.
The shotgun barrel will have a “x1” beside the card damage ( a “fib” )
The ricochet barrel will have the highest damage : ~50000-60000 at level 50
The third barrel will have extremely low card damage : ~500
I’m not sure if you’re on a console, but as an X360 player you can just exit out of the game without saving it (making sure to enter and exit Ore Chasm before that), and then re-enter the game. It was by this method that I got what I deemed the perfect Fibber for the E-Techromancer (shock, and the ricochet variant).
(I will have to consider the slag ricochet variant for Gaigetrap though. Glad that was mentioned because I actually want a grenade mod that sinks teeth into health bars.)
Yeah I currently have the shotgun barrel and it’s hard to hit anything that is moving.
Also I forgot, the Redundant prefix will show x2 which is legit. It shoots two pellets at a time.
Just in case you might mistake a Redundant ricochet ( 50000 x2 ) for a shotgun ( 500 x1 ).