I have recently come back to the game after only playing it for 30 levels at launch. I am having a great time. I thought it would be helpful to share some of the things I found not obvious. Please feel free to correct me and/or to add to this list.
1) Starting at 16 you can begin doing the "Duty Roulette: Low Level", which gives a significant amount of XP the first time you complete it each day. You will want to use it everyday for whatever main spec you are leveling. Also, at 10 you can do "Duty Roulette: Guildhest" once per day for about 2 FATEs worth of XP.
2) A lot of the dungeons in this game are opened by doing the main story quest (blue !), but not all of them. Some require doing a side quest. Below is a list of dungeons with the quest you need to unlock them.
http://ffxiv.consolegameswiki.com/wiki/Dungeons
3) If you can't progress main story because the next step is a higher level--and then you forget where that quest was once you level up, you can look in the book next to your bed in the inn to see what was the last step you completed, then google it to find out the next quest (and quest giver). If there is a better way to do this, I'd like to know.
4) After you complete this level 17 quest, you can "hire" (first one is free) a retainer at the Retainer Vocate in any of the 3 major cities market area. These act as a bank, and they can sell items for you on the market. You can summon your retainer at a bell (in the market and in your inn room).
5) Items with a little dot in the top right can be dyed---but only after you do this quest.