In which order should I get the artifact, I know I should do helm last, but which one is better to use first, Cloak or Amulet?

Also, anything that hurts equipment in DCMA?

Cloak > Amulet > Helm is the correct order to play them in ifyou have all three. The only card that hurts equipment in DCMA is Multiverse power battery.

Personally, I play Cloak first because of the untargetability and the defensive pump.

As far as Equipment hate in DC Modern, Multiverse Power Battery is the only card I'm aware of that hurts equipment.