@JC Addressing your questions in order:
Which one to go for...
In general, the weapons higher on Zig's list (i.e. closer to the top of the page) are stronger and are the ones you eventually want to own. In particular, the Klauz weapon series is Best in Slot for most classes at the moment.
The Klauz series is actually an upgrade from the Agile series which is really strong in its own right so this is the weapon I'd target first as you need an Agile enhanced to +35 to make Klauz.
However, as you noted, it will take a fair bit of time to grind for the materials for Agile and Klauz so you'll want something strong to help you while you work towards that goal.
You could work on the Puras & Steel series, but they require a lot of the same materials you need for Agile & Klauz so I'd probably skip those at this point.
The Rivalate series is a fine choice and can compete with Steel in terms of damage if you unlock its "plus potential" at Monica/Dudu using the Change Weapon Potential menu option. However, unlocking the plus potential will require some resources (Luminfragment Emel) you need for Agile and creating the base Rivalate will eat into your rare crafting material (e.g. Plamnia) / class Ex-Cubes that you'll need for Agile / Klauz.
You could move down to the Trailblazer or Atlas Ex series as these don't require any of the materials needed to make the endgame weapons aside from basic Ex-cubes. The reason to go for these would be because of their potentials (Trailblazer refills all PP with a cooldown and Atlas Ex prevents you from dying once per mission) as well as the S-Grade augments they can utilize (in particular the Atlas Ex can use S4 augments which can be super useful depending on your class). However, in terms of damage you can do better than these unless you unlock their "Plus Potential" which will again require resources you'll later need for your Agile weapon.
So if you're low on those materials and/or don't want to spend the meseta to buy some of them off the Player Shop (e.g. Plamnia/Plamdest/Plamgrimo can be traded), your best bet is to use some of the gear you can get from NPCs on the ship.
The Croesus series from the first 15 Star Collection Folder is a great stopgap option that can use S1 - S3 augments and has a hidden +15% dmg boosting potential which makes is stronger than the Atlas Ex and Trailblazer unless you unlock their Plus Potential. As a result, many players say that a Croesus weapon is the minimal you should have when entering endgame / UH content.
There are also certain 14 star weapons from the Unique Weapon Badge Shop and Rising Weapon Badge 5 Shop that have unique potentials which make them competitive options as Croesus alternatives depending on your class. I believe the Rykros Staff (Harmonizer) and Jupiter Tullus (Soaring Blades) from the RWB5 shop are still endgame viable. But I've also heard good things about the Lavis Cannon (Wand), Eternal Psycho Drive (Rod), Dual Bird (TMG), and Spread Needle (Rifle) from the RWB5 shop...and possibly Gear Experience (Knuckles). And then from the unique badge shop you'll want the Serpent Prenzer (Jet Boots) for sure, but I'm not confident on anything else from there (though the Genon series can be useful as specialty weapons you switch to for regenerating PP when combined with certain S-grade augments like S2 and S3 Lucent Adversity).
What the list of materials even means and where do I get them...
LazerRay gave a great link describing the materials and outlining where they can be found!
And if you participated in the Mop-Up OP: Endless Nightmare Limited Quest campaign that just ended then you might have gotten some of the super rare materials that are required for making a few of Zig's weapons:
- 3 runs granted 2x Chronos Eternistones (Atlas Ex component)
- 6 runs granted 2x Founder's Amphrite (Trailblazer component)
- 9 runs granted 2x Key Rivalate (Rivalate component)
- 12 runs granted 1x Powerstone Graea (Klauz component)
OK, so let's add a little more context to the materials you need for an Agile weapon and a Klauz weapon...
- Plamia x100 (or Plamdest/Plamgrino depending on the weapon type)
- Emerard x50
- Darkstone Deimos x20
- EX-Cube x200
- Luminfragment Emel x200
- Ultimate Booster x30
- Darkweave Agile Edge+35 x1
- Diard x50
- Darkstone Deimos x150
- Powerstone Graeae x1
- Lumincrystal Grania x4
- Class EX-Cube x300
You can get a Powerstone Graea and 30 Darkstone Deimos from the current Mission Pass so I'd definitely try to progress that this week before the season ends. If you really want those materials and have a lot of Star Gems you can also buy Mission Pass tiers for 25 SG each IIRC.
Plamnia/Plamdest/Plamgrino, Emerard, and Diard can be bought on the Player Shops and can be earned directly by Dismantling 14 and 15 star weapons in your Personal Quarters. Plamnia comes from Melee weapons, Plamdest from Ranged weapons, and Plamgrino from Technique weapons. The visiphone also notes that you can get Diards directly from Divide Quests.
Darkstone Deimos will drop from the Primordial Darkness Urgent Quest (SH or higher) and you'll get 9 each time from an UH run if you get an S rank. You'll also get stones as Title Rewards depending on the numbers of times you've cleared the UQ.
- 1 clear = 10 stones
- 20 clears = 20 stones
- 30 clears = 30 stones
- 40 clears = 40 stones
- 50 clears = 1 Powerstone Graea
I've also heard that they're dropping from the new solo Ultimate Quest where you face off against Sodam, although I haven't started that grind yet myself so I'm not sure if those rumored drops are from the boss itself or the titles associated with clearing on each class (10 per main non-scion class on your first clear).
You can get Ex-Cubes directly from quests, indirectly through converting rare drops in the Swap Shop, or from the Misson Pass. You can also get some Class Ex-Cubes from the Mission Pass as well as directly through overleveling your character (i.e. leveling up once you're at max level) or from certain missions like Tokyo Rainbow Keys, the solo Ultimate Quest against Omega Masquerade, the Endless quests, etc.
Ultimate Boosters can be purchased from some of the NPC vendors (Photon Booster, Divide Medals, RWB5s). You can also get a bunch upon completion of the latest Extreme Quest (Risk Realm) as well as from certain UQs on UH difficulty (1 guaranteed per solo Profound Darkness clear, Mining Base Defense 5 drops more depending on your grade, a lot of the seasonal UQs have a chance to drop them, etc.). You'll also get 5 each week from earning a total of 250,000 Divide Points via Divide Quests.
Luminfragment Emels come from Divide Quests and in particular the reward boxes you can earn in the Covert Ops stages (the one where acid rain starts falling 3 minutes in). You'll get a box for each of the "virtual devices" you disable which are the golden totem-looking things that give you a slight buff in the mission when you interact with them. So if you want Emels it's worth sticking around for as long as you can survive on those stages, especially if you get the Life Points Disabled boost for that stage or have your Dark Blast available - the Elder form can heal even in the rain. You'll also get some Emels from the boxes after you clear all 5 stages in a Divide Quest and you'll receive 50 Emels each week when you earn a total of 350,000 points from Divide Quests. You can also get an additional 50 from a title the first time you earn 500,000 points in a week and can exchange 10 Divide Medals for 1 Emel through the NPC vendor on the 2nd floor of the Shopping Plaza.
Lumincrystal Grania are pretty rare drops from Divide Quest completions in my experience. However, you can exchange 200 Luminfragment Emels + 350 Divide Medals for 1 Grania in the Divide Medal exchange in the Shopping Plaza. But the easiest way to get your first Klauz weapon is through title rewards. In particular, you'll get 2 Granias the first time you earn 3 million total Divide Points in a given week. And you'll also earn 3 Granias the first time you clear floor 35 in a Divide Quest.
I know this was a lot of information, but you should be able to get an Agile weapon in a couple weeks of casual play. However, enhancing that weapon to +35 to make your Klauz will take longer as the usual method is to use Enhancement Cap +1 items which are pretty expensive on the Player Shops atm. You can get these caps as a rare drop from Tokyo Rainbow Keys or via some pretty expensive exchanges in the physical Swap Shop in the Shopping Plaza. You can also raise the Enhancement Cap by 1 each time you infuse another copy of your Agile weapon into your original, but this will take a lot of resources to buy multiple copies from Zig. If you're willing to wait, I've heard that Enhancement Caps will be available from the upcoming Challenge Mode Quest that hasn't been released on Global so you could get them there or wait for prices to hopefully drop on the Player Shop.