Remnant: From the Ashes

Armor Sets require a piece belonging to 3 parts.
Helmet.
Body Armor.
Leg Armor.

I'll list below the first 5 full pieces I was able to get.

Hunter Shroud/Trenchcoat/Pants - Beginning outfit for the class I picked, so you already have 1 based on the class you picked.

Cultist Hat/Duster/Britches - Purchased from the blacksmith in the Ward.

Scrapper Helmet/Bodyplate/Workboots - Purchased from the blacksmith in the Ward.

Twisted Hood/Cage/Tassets - Found in a random instance on Earth, where some roots went up a Crane, prompting me to hold off a wave of enemies. The reward being this set.

Osseous Helm/Husk/Kilt - In the Scouring Waste, on Rhom, you will eventually come across a man named Wud, who is sat beside a dog, and a shortcut leading back to the start of the Rhom area. He'll offer some items, as well as secrets for 100 scrap each. Pay him around 400-500 scrap total, and he'll run out of secrets. This will result in him telling you he'll give you armour instead. So load up his wares once again, and the full set will be there for a few thousand scrap.