Sounds like you need to try to find a group for Second Coil of Bahamut, if you want a challenging experience that pushes forward one part of the story. It's a very mechanical raid though. Mistakes are punished heavily and everyone has to know what they're doing.

Probably the best non-raiding way to progress your gear right now is via hunting and using sands/oils to upgrade your weathered gear. You'd need to find a linkshell (or multiple) that are doing this, as there is typically a group within each server coordinating to kill A and S ranks when their spawn windows open. There's plenty of tools out there now to track Time of Death for these, so it's just a matter of finding a hunt party that is doing more than sitting in town waiting for people to announce when a NM is due to spawn.