Which server are you on?
It's a lot of fun. Especially after you get a chocobo and can freely roam the map. Run up all the way north for the Svari quest. There will be lots of people taking on the giant dragon, pretty epic. It's an all server quest so lots of people below level 60 will be there. Try not to die and get into whichever party you can.
The other really awesome fate, server quest, is Odin and Behemoth. Hella' hard but it's fun seeing everyone go at them. Fates are quests that happen on the open map so everyone can attend regardless of level.
The dungeons can be pretty fun in the beginning. Your first 24 man dungeon will be amazing as you infiltrate the final base and defeat Ultima Weapon. If you've ever played FF7 think of the bombing mission except on a huge scale.
Don't worry about which class you're going to choose as you can switch back and forth freely, the only thing that you won't be able to change is your race.
Dungeons are hard to get into if you're not playing a healer/tank, servers are bloated with dps class types. I mainly played as a tank and healer, you'll have more responsibiliti es as a tank since you need to control the flow of the battles. The healers just need to pay attention to healing the tank and everyone else once in a while. It's more difficult playing tank since you could really screw up the run, a lot of ****s will give you shit if you do screw up which is why there aren't a lot of people playing that class. Pressure is there.
Once you get better try to create macros for combo attacks/buffs.
Items from dungeons can be competed for via a random roll, so you people don't have to compete for the finishing blow or camp out at certain places.