REALISTIC progression in gear would be as follows.

You'll want your full AF starter set ( of ocurse, not hard to miss this. ) and make sure you kept up with grand company promotions up until serg. Buy the level 44 green GC weapon. Trust me. It'll help.

With starter af and a green 44 GC weapon, you can do wanderer's palace for iLvl55 armor and a chance for weapon upgrade as well as running HM Ifrit side by side for a weapon drop chance.
HM Ifrit is not very hard at all. Avoid clones, and the plume dance.

Plume dance is inside, run outside, go back inside.

You can also easily do Caestrium/Praetorium for tome farm to get more gear.