I'm not sure where you're located, but here in the US you can build the building you're describing (a square house with a gable roof, without eaves if you want the roof to terminate at the wall) pretty easily with regular dimensional lumber framing.
Barndominiums generally imply steel framing and requires heavy equipment, at least to hoist the steel beams into place. They are less easy to build and maintain than a stick-framed home, in my opinion. A simple incarnation of a latter could be thrown up by two hobbyists, if it's small enough.
Lstiburek's "perfect wall"[0] may be of interest to you. Simply put, layered from the inside to the outside, it's drywall, wood studs (with batt insulation), sheathing (plywood or OSB), plastic house-wrap over the sheathing to serve as an air and vapor barrier, some depth of external insulation on top of that in the form of boards, then finally the exterior cladding.
[0]: https://buildingscience.com/documents/insights/bsi-001-the-p...