Something like these then?
They would be suitable for the floor framing, yes.
But using triangular trusses as gambrel side framing gives more side-to-side strength.
You end up with a double-thickness truss, every two feet. As I said, it's costly that way, but it should be quite strong, and the trusses are more commonly available.
It would also be nice to have a crane for the assembly. But even if you don't, I think these could go up fairly easily.
Good Luck on having a proper barn again!