The item brand is located just below the name of the item while in your inventory, the majority of starting weapons are Spacer's Choice however finding the clothing and headgear can be tricky at the start of the game. Head to the first town, Edgewater, then go to the General Store and purchase the Mining Helmet and Worker Outfit. Both are 50 bits, if you don't have four Spacer's Choice weapons you can also purchase them from him, but I had more than enough from killing enemies along the way. The Hibernation Suit that you start with is labeled as a Spacer's Choice but the achievement did not unlock for me until I took it off and wore the Worker Outfit. You can also save and reload after you get the achievement if you don't want to spend your bits on the clothing.
Edit: The Hibernation suit may work, try equipping it with the rest of gear first, then buy the Worker Outfit if it doesn't.