I'd work first to get Philosophy gear (full darklight) ASAP, make sure nothing is below i70
Currently your 'Best in slot' gear is going to come from a mixture of Mythology gear from Rowena's NPCs in Revenenants Toll - Mor Dhona.
You purchase this with 'Allagan tombstones of Mythology' from doing your daily roullete (see below)
So if you haven't already unlocked The Binding Coil of Bahamut, now is the time, as your mixture of i90 gear will come from Rowena and The Binding Coil.
PLEASE CHECK online what is best in slot, don't get a full set of Mythology gear, it's usually a complete waste as some items are better than others.
Hard Mode Primals
You need to beat these to gain access to The Binding Coil of Bahamut, seek out a party to help you get through this ASAP!
Crystal Tower [Follow your main story line and pick up where that left off (try the waking sands)] once per week you can participate in the 24 man raid and get ONE item per week. Whatever you lot on and drops to you LOCKS YOU OUT from lotting on anything else will Monday 3PM GMT.
This gear is i80, it's a fantastic stepping stone for getting into The Binding Coil of Bahamut and extreme primals, chose
Extreme Primals
Extreme versions of the primals are avaliable;
Ultima, Garuda, Titan, Ifrit. You're going to need at least full darklight for this is pretty much a nessecity as a minimum.
Dailies & Daily Roullete!
Daily Quests are now avaliable from the Amaja'll and Sylphs, check the Grand Company HQ's in Ul'dah and Gridania for the quest-line
Daily Roulette is simply a random low or high level dungeon for a daily tombstone reward, you can get an extra chunk of philosophy/mythology everyday doing your high level dungeons, and philosophy from low level dungeons and your main scenario. (Guildhests are great for gil+GC seals)
The reward is once a day and resets at 3PM GMT.
PVP!
Go to the Maelstrom Command in Limsa Lominsa for a breifing on Player Versus Player and the quest-line to unlock it (fairly short).
It's a fairly bog-standard arena based fight 4x4 parties works quite nicely (except for the gear issue)
I recommend if you really want to try this to craft some pvp gear and do the low level 30-40 ones.