This forum seems very slow, and this game has a very steep beginner's learning curve. I can't invite you to the linkshell, but I can provide some advice for the new player:
The menu and movement can be annoying, but I assume you have that figured out already. In case you didn't know, here is some information you can use:
The Residential District on the map will take you to your mog house. This is like the stash or personal bank in other games. It also allows you to change jobs, and you can decorate your house as well.
The auction house is marked by a gavel. You can buy and sell things here. This is a blind auction in which you bid on an item until you bid over the price set by the seller. It is completely different from the WoW AH. The best way to bid/sell things here is to mimic the prices that previous sellers have sold things for. You can view this information in the AH menu.
As a mage, you need to use scrolls to learn spells. There is a magic shop in every town, in one of the districts. You can buy several beginner scrolls here. Beginning melee classes can find armor sets and basic weapons at the weapon shop too. These shops are marked on the maps.
No matter what city you started in, there is a guard at the gate before you go out of town. Get signet from this guard. Signet lets you earn conquest points for kills. These points let you buy things later. Signet will also let monsters drop crystals. These things are a good source of income for new players. A stack of crystals can sell for 2000 gil or more on the auction house.
Register and get your destrier beret if you have the abyssea ultimate collection. I am not sure if linking is allowed on this forum, but if not, go to the ffxiclopedia website, type in "destrier beret" to search for it, and a guide will pop up showing you how to get it.
When you zone out of town, you will be in a starting area with weak mobs. There is a floating book (Field Manual) near the zone. This book gives quests to kill x number of mobs. Accept these quests and set them to repeat upon completion. Completing these quests will give bonus exp and some tabs. You can spend these tabs at the book to buy regen (restores hp over time) and refresh (restores mp over time) buffs. You can also buy warps back to your home nation with tabs.
Quests and missions are secondary nowadays. Quests usually give an item or scroll for a reward, and missions are just for story and the airship pass. There are no floating yellow markers to tell you where to go and where to turn things in, so don't worry about doing them now. Work on these when you are higher level and more familiar with the game.
At level 15+ I would advise going to Gusgen Mines if you are able to get there. You can check the ffxiclopedia site for zone connections and how to get there. There is usually a large group of people doing page one of the book quest inside. If you do not have an escort, getting there may be hard if you are from Windhurst.
I can add more if I have more time.