Hello,
Since a lot of new players - myself included - find themselves disoriented and unsure of how to get things started when joining CoA, I'm going to try and put together a small reference guide. Please correct me if any of the information is wrong or anyone would like to add anything else 
Gear and Loot:
Cores:
These are the five kinds of cores you are guaranteed to get at the end of most Arcadia-Custom instances ranking from lowest to highest:
Weak Core: Hall of the Demon Lord (HM): Same prequest as normal mode to enter.
Temple Core: Secret Temple of Tikal - Prequest to unlock this and higher custom instances.
Fire Core: Inferno of Divinity
Ice Core: Gorge of the Ice Giants
Earth Core: Realm of the Forgotten Legends (ROFL)
There are two things you can do with your cores:
1. Create a weapon: You need a certain combination of cores and a Sealed weapon (obtainable in ROFL) in the arcane transmutor in order to create a golden weapon.
2. Get an almighty core: After clearing ROFL, you need to do an event in order to unlock an NPC in the chamber of elements. Once unlocked, this NPC will offer you the option to trade 5 (one of each) cores in exchange for an almighty core. You can do this once a day and once you have 10 you can exchange them + a piece of red ROFL gear for an upgraded version of that gear, also referred to as a golden pull.
Core Conversions:
You can buy core conversion recipes at an NPC outside Atlas - these require alchemy level 100 (covered briefly below). You cannot get a higher tier core from a lower tier one, but you can convert cores down by one, two or more steps based on your needs.
Fragments:
Fragments are required to buy gear/stats from their respective instances. These drop at the end of Inferno of Divinity (Molten Fragments), Gorge of the Ice Giants (Frozen Fragments) and Realm of the Forgotten Legends (Buried Fragments).
One kind of fragments are exchanged in Atlas + a relatively high sum of Arcadia Coins in exchange of a stat of your choice from that instance and for your fragment class:
Protector: Stamina
Pain: Strength
Agility: Dexterity
Knowledge: Intelligence/Wisdom
There is no corresponding option for ROFL as it is the current end-game instance.
The other kind is exchanged in Chamber of elements and those are called Plate/Chain/Leather/Cloth and Charm (Accessories).
In addition to being end-boss drops, these kinds of fragments can also be bought from NPCs in chamber of elements for coins. To exchange you need:
A Fragment
A piece of gear (purple from boss drops or also bought by NPC for instances lower than ROFL)
100 Lava (Inferno)/Ice (Gorge)/Earth(ROFL) dust which can either be farmed in the chamber of elements or dropped by mobs in the instances.
10 Lava/Ice/Earth Shards which drop from bosses and are usually collected by one person and split at the end of the instance or however else the party chooses to handle them.
With this, you can get a stat and/or a Red piece of gear which would be the upgraded version of its corresponding purple.
It is possible to roll for something other than your main class, but you need to call your choice before the last boss: Fragment - Stat - Weapon (if RoFL).
Stats:
Custom instances drop purple stats at the last boss or purchased by the above method, their names are:
Arcadia-(x) - from HODL, HOS HM
(x) of Tikal - From Tikal (or purchased cheaply for coins in Atlas)
(x) of Divinity - From Inferno
(x) of the Ice Giants - From Gorge
(x) of the Forgotten Legends - From RoFL
It is possible to join parties for HoS and Tikal with relatively low-end gear, the other stats are more difficult if you are just starting out, however.
Some alternative solutions that you can get by yourself:
of Dawn and of the Storms stats can be obtained with Phirius Shells (from minigames or IS) from NPCs standing on a ship East of Atlas
XVII stats are affordable and can be obtained in some high-level zones.
Random Attribute Extractor stones do come on sale often so don't be too afraid of statting somewhat poorly and having to restat later on if you are not getting help.
Crafting:
Since Alchemy 100 is a near-requirement for anyone aiming for end-game, here is some helpful information:
The memento vendor in Weeping Coast sells materials (and rare materials like straw mushroom and bison grass etc.) up to level 60.
All following materials needed to get to 100 can be obtained with mementos from Black Codex NPCs around the world.
You need approximately 8000 mementos to level alchemy from 1-100 (I imagine other crafts are in the same ballpark)
To maximize your efficiency you can:
Try to get alchemy furniture in your house when they are on sale, the maximum bonus is 1000 and helps with XP and crafting speed considerably. If you cannot afford them, then you can craft in someone else's house but you would only get the speed and not the XP.
Use Production XP and Speed potions from IS as well as the crafting XP Item set skill from the level 60 craftable guardian set.
Have your mementos ready and locate and mark the NPCs and trainers before starting for minimal hassle when crafting.
Have Home sweet home handy.
While some of the cooking/alchemy recipes are still viable, do not expect to make much profit with them as most important recipes have improved level 100 counterparts sold outside of Atlas and craftable for materials purchasable with Arcadia Coins.
Making Your First Diamonds:
This is maybe one of the trickiest parts for new players who join the server alone. The unfortunate truth is it will be very difficult to make a decent amount of diamonds as a complete starter and without some capital first, but it is not entirely hopeless. Here are some things you can do:
The crafting route: Farm mementos in Grotto of Horrors (HM) and level your alchemy/cooking and earn enough coins to purchase some recipes - this way you can make some diamonds by running only the lower custom instances. (not very recommended as you will need your coins, but it is an option).
The Grindy gold farming route: farm items and vendor them for gold and sell your gold on AH for diamonds. Find an instance with a decent amount of mobs that you can comfortably farm - the additional backpack spaces, traveling merchant and fast pet-looting make this a bit less hellish. You will not make an insane amount of diamonds with this either, but again, it is something you can do on your own.
Tier stone farming route: this is perhaps the more reliable solution for income if you're willing to grind, as buying charges and puris while they are in promotion allows for a decent profit margin. You do however need a starting capital for this, however small.
The card farming route: this being the way to go has been a myth in my experience, some cards do sell for a little bit, but effort/reward ratio isn't too favorable. Some of the cards obtained from events can go for a decent sum of money, though.
The XVII and shell stats do sell, however slowly.
Additional Information:
NPCs in Itnal Camp in Atlantis will give you some daily free rewards.
If you want to jump straight into the action, WL/M is always a welcome addition in parties as a support class. All you need to start is to be able to survive, and know how to keep the party buffed. A good starting position if you want to go this route is to grab healer level 80 gear when you start your character as healer gear has a lot of HP. This + some food and some minor changes should allow you to run some of the instances and start farming gear and stats for yourself.
Atlas Defense is an instance special to Arcadia: it is open only on weekends and can be joined once a day. It's a 6-player instance and has 3 modes of difficulty.
In order to access the instance you first need to get motivated by an NPC called the wanderer. You will sometimes see in chat the zone he is in, or you can try and access the portal and get information about his current zone. His spawn locations can be found here. The instance drops a currency called Atlas Scrolls, which you can exchange for gashas at the same NPC later on for a chance at some rare cards, some gold, or if you're incredibly lucky a set of special golden wings.
The Shadowmoon Merchant: You will see a message in chat every 2 hours saying that the shadowmoon merchant has appeared in X zone and is selling goods for Y currency. This vendor sells some useful item shop items like phoenix, home sweet home, house energy, plussing stones etc. for various different currencies. He has a limited supply (first come first serve) and despawns after 20 minutes. He has a set number of spawn locations per zone. The bad news is people will typically not share his whereabouts as this could basically ruin the whole thing if people just port and take everything and leave nothing for others. The good news is, it's a hassle so most of your competition is likely to be other newbies.
Elite Skills: You only need to do your 60/70 elite skill quests on one class. After this, all you need to do is speak to the NPCs again on a new class in order to get all your elites. Some of the items required for elite skills are available on IS and are periodically on sale.
You can have all 10 classes on CoA, you just need to change your race/gender and pickup the class then you can keep it once you switch back. If you go dwarf, you will remain male when you change again so you would need a gender change ticket if you want to play a female character. Unique class combinations like Champion/Knight or Priest/Druid have recently received elite skills on CoA, and constant rebalancing and adjusting is being done in order to attempt to make most class combinations viable.
Happy adventuring!
really good job on that .
and added
Also Rogue/Champ could be used as such, but it's a bit too weak with starter gear I guess.