I thought I would update this thread with some more things I've found / been shown, as I've received a lot of help these past couple of days. (this is also my attempt at note taking for that guide I promised...) =D
First off, there are some great guides on the left-hand side of the lodestone. Some of these are VERY basic, but of particular note to me was the guide about Grand Companies. http://lodestone.finalfantasyxiv.com/pl/index.html
Main Site http://lodestone.finalfantasyxiv.com/pl/guide/cont01.html
Grand Companies Guide
There is also an excellent item database site called mooglebox. Aside from being simple to use, it has an AMAZING tool for locating packs of mobs in a certain level range. This is incredibly useful when trying to figure out where you should be leveling. http://mooglebox.com/includes/
Main Site http://mooglebox.com/thanalan/index.php
Mob Location Tool
Gamer Escape is a pretty good Wiki, with mostly up to date information. It can be a little difficult to navigate, but I've found some good stuff on there. http://ffxiv.gamerescape.com/
Mozk Tabetai is a very slick item database, that will tell you pretty much everything you want to know about an item (great for research too) http://mozk-tabetai.com/
And of course, over on gamefaqs, Arcell is keeping mostly up to date some class guides for each class. Some have even been updated this year. http://www.gamefaqs.com/pc/960613-final-fantasy-xiv-online/faqs
That should do it for the sites, now just a bit of advice.
Don't feel the need to burn through your leves. While they are great for quick XP and money, they stack up to 99, so if you can save them for later, higher level missions, you can get more out of them. That said, if you feel the need to take a break from grinding go ahead and do some, they are pretty fun and can be challenging depending on what level you are / what difficulty you choose.
Do all of the starting quests in all three cities. They offer good money rewards, some new player items, and a little bit of XP. They will also get you used to traveling around the various locales. Keep in mind that if an NPC tells you they have marked your map, what they mean is that if you pull up the quest in your journal, there is map button you can hit to see the locations of the objects. They did NOT mark your main map (although I wish they would).
Make sure none of your gear needs repairing before leaving town / camp, you don't want it to break and lose the benefits of it till you get it repaired.
If you can't find a place to put your retainer in the market ward, rent a stall. When you kick your retainer out of the stall, he / she will be standing in the ward. Also, if you list an item for 999,999,999, your retainer will never leave the ward.
And finally, if you see a giant dragon-like lizard sitting in the middle of the road in South Shroud, RUN! He WILL one-shot you for 2500 damage and send you all the way back to Thanalan. =D
Well, that's all I've got for now. I'll keep sharing as I discover more things useful to a newb, so that others coming along after me can maybe get a bit easier of a start.