I'll give it a try.

'Relic' weapon is a quest weapon at lv 50. You go through a series of quests requiring grinding out various aspects of the game to upgrade the weapon between stages. 'Anima' is the same thing, but at lv 60 with a better weapon. You can ignore relic and just work on anima when you get to 60. The anima weapon ends at ilvl 270, making it tied for second best weapon in the game ilvl-wise (there is a 275 that's higher). I haven't done any of that yet, so I can't speak from experience.

Poetic tomes are a form of currency you get from completing lv 50 dungeons/trials/potd (potd = palace of the dead). Poetics buy ilvl 120 gear. Lore and Scripture tomes are from lv 60 content and potd. For potd, you must be lv 50 (outside of potd) to start getting poetics, and lv 60 to start getting lore and scripture. Lore buys ilvl 230 gear and scripture buys ilvl 260 gear. The gear you buy can be upgraded later.

Gathering classes get many of the materials that crafting classes need to craft things. You can sell that for gil or use it in your crafting classes. Some of the equipment crafters make is great stuff, but you also have to consider glamours and furniture for housing. While that stuff may not be objectively useful, it is highly desired and fun! Also, gathering classes can find treasure maps in lv40+ nodes, but I don't know how useful those are yet... almost to 40 on my miner though, so I'll get to try it soon.