Where should the ground wire connect in a new sub-panel?
You don’t say if the sub is in the same building or not. If it is in the same building, use the existing ground as separate grounding systems can create a problem in the same building. Since you are going to all the trouble to put a sub in I would bump the size a bit--10 awg only provides for 30 amps for the sub. Bump up the wire size and have some space for additional circuits later. I don’t waste time on anything less than 50 amp subs for the most part.

Bring the hot, hot, neutral and ground from your main panel to your sub and make sure the sub ground is isolated as you mentioned.