Quests first, even the side quests unlock content on occasion.
Personal opinion here is to leave eidolons last, better to use easier to farm arcanes from Zariman/mirror defense/lua for now
Incarnon weapons, but those are a ways off given you need steel path. Zariman after quests also has some weapons.
All but the absolute trash frames, weapons will carry the game on their own. Depends on playstyle. Me personally will only use frames with 90% DR or projectile reflection since i dont like dying all the time.
Up until level 180-200 meta weapons with as much upfront damage as you can muster, after that viral slash.