Make sure to pick up at least an i55 weapon like your grand company weapon, but if you have money to spare or it's not too expensive on your server the i70 crafted weapon will serve you well for a good long while until you can get your relic or something similar or better. I wouldn't stress about filling out your character entirely on dungeon drops. Take what you can get and save your myth to buy i90 gear which will be sufficient for everything up to the current new content.

Playing a BRD, you really lucked out, too. Their myth set is phenomenal stat-wise.