The most logical path is to get the level 55 barbarian's Bardiche simply because you can use it to start the relic quest after you have finished the last 2 story dungeons and it will be sufficient enough to get you that far. Considering you have to hand the axe in after melding it for the quest you will require a secondary weapon for the Amdapor keep and primal parts following on from that, the easiest weapon to get would be the level 55 grand company weapons since then it doesn't cost you anything to use.

The hardest part will be Amdapor keep simply because you will be the only tank for that dungeon and most likely very much lesser geared than the other people you are with.

If you don't have the grand company rank or the seals (even though it would be very easy and quick to farm them) a HQ vintage bill (expensive to buy but very easy and cheap to make) probably the best sub 50 weapon and might possibly be enough to get you past Amdapor where doing ifrit, garuda and titan will mean you will likely have a bunch of high levels doing most of the work for you at that point you will have completed the relic quest line and gotten a level 80 weapon.