Guild Wars 2

Can someone explain to me which ones are important and why I should get them for my ele? I’m a bit new so I don’t know everything yet.

It depends on what you’re crafting for.

For the crafting-required equipment that you will use late game at level 80 (ascended weapons and armor) I would recommend Artificer for Staff/Scepter/Focus (or weaponsmith if you use dagger/dagger) and Tailor for your light armor.

But crafting also provides 7.5 levels from 1-400 and if you’re crafting just for easy levels, you will want chef, artificer or jewelcrafter.

Artificer for your weapons (except daggers, those require Weaponsmith)

Tailor for your armor.

Jeweler for your trinkets.

Chef if you want food.

Btw none of these are necessary. You can buy all of the weapons/armor/trinkets/food you need from NPC merchants and the trading post.

Well.
The first and very wrong idea behind crafting is “I will make my own stuff” (thats why I always start crafting in any mmo and I always discover I was yet again wrong).
The only good reason you need to craft is
1. you like crafting
2. you want ascended stuff
You can get everything but ascended stuff much easier than to craft it.
Armor and weapons – grind dungeons, namely CoE, which gives exotic berserker armor and weapons AND 1 gold per run.
Trinkets – do achievements for laurels and buy ascended trinkets from laurel vendors. These will do the largest difference anyway. Just compare stats of exotic vs. ascended armor and exotic vs. ascended trinket! Do not waste your laurels on ANYTHING except trinkets until you have full trinket set on ALL your lvl 80 alts.
That said, I have grandmaster in weaponsmith, armorsmith and hunstman, leatherworker at some 460 atm, and at least 400 in everything else. And yes I wasted a lot of resources and the valuable laurels on crafting because I like it for some reason. If you, too, like crafting, and that ele is your first alt and you are considering what will be your first craft selected, then think about your alts. Ele is not bad at all but I guess you might end up with at least one war and guard (useful both in dungeons and WvW), which means you will need ascended stuff from armorsmith and weaponsmith (and ele needs the daggers).
Cooking is a very good choice but pretty expensive. However making stuff which would give you bonuses to experience, gold and magic find as you level might help. Jeweller is another universal crafting discipline, but it is somehow obsoleted by the ascended trinkets you can get for laurels.
So, unless you are craftin obsessed do not rush it. Just gather and keep every craftin mat you can get and wait. Do dailies and mothlies for laurels. Do dungeon stories as you level, nobody will kick you from story (at least I hope, people can act… strange sometimes). Once you hit level 80, get some at least yellow stuff and start doing dungeon explorables (you can train champs in Frostgorge if you lack the cash for rare equip, which is likely). Remember that completing you char story gives you rare (yellow) headpiece and a token which buys you a rare weapon from quartermater at Trinity fort.
About in time you will get some exotic pieces from dungeon, you will get enough money to start levelling crafting. If you want to do ascended which you likely want, save karma for obsidian. You can buy obsidian only at Balthasar temple (cathedral of Glorious victory) which is seldom open since the quest is pretty tiresome and can fail at the very end. But you can look at http://www.gw2state.com/temples.html and guest at a server where it is open and then I recommend to spend all your karma for obsidian.
Good luck, you will need it. Oh. NEVER sell linen if you want to do ascended armor.

Oh, and one more think: always keep a full set of gathering tools and salvage kits with backups on your char and do not be lazy to harvest everything you will see. Salvage anything you find and do not need or want instead of selling it.