Mind share with us what's your rooster and at which domain you struggled? Some domains are with PITA debuffs that will mess up with your current party setup if you don't have many replaceable units. Eg cannot use fire to melt ice or you will get damage, so you will have to use electric to slowly break the shield.
Resources are scarce so you don't really need to farm Artifacts domain at this level yet. For me I was using all blue and purple until reach AR45 which unlocked LVL90 domains with guaranteed gold drop. Prior to that I only farm Weapon Domains(max level unlocked at AR40 IINM), World Bosses(Pyro Cryo Flower, Anemo Electro Cube etc) and Mora/EXP Book Leyline clouds.
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You don't need to specifically farm for artifacts now, but you still need to level up the artifacts you equipped. Blue and purple one will do, you can get most of them from World Bosses mentioned earlier.
For DPS unit just pair any good main stats one and you can safely ignore the 4 set bonuses, for now. Goblet slot always goes for matching Phy/Pyro/Hydro/Cryo/Geo/Anemo element DMG bonus as main stat, headpiece crit chance/crit dmg if possible.
For support units, just get them any 2x Exile + 2x Scholar and leave them at level 1. For timepiece slot go for Energy Recharge as main stat and max level it.
And don't forget to level up your Talents as well.
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Edit: Added more info