A subpanel can have its own grounding, isolated from the ground of the main panel. I used 6 gauge for the ground, bolted to the center of a buried 2'x2' steel plate as is done for swimming pool installations.
For 20A circuits, 12 gauge solid core, not stranded, as a minimum should be used, but it all depends on the length of run. I did some overkill by running 10 gauge solid core for everything, which is not easy to work with but can be worth doing. Insist on the same size for the ground conductor. Twist the wires together using an electric drill before pulling them to prevent vibration in the conduit.
For 20A circuits, 12 gauge solid core, not stranded, as a minimum should be used, but it all depends on the length of run. I did some overkill by running 10 gauge solid core for everything, which is not easy to work with but can be worth doing. Insist on the same size for the ground conductor. Twist the wires together using an electric drill before pulling them to prevent vibration in the conduit.