Grounding new service
Ok, first off, if you have copper or metal water pipe coming into the house you MUST use it as the primary grounding electrode. This means you have to connect to it within 5' of where it enters the house and jump around any meters and plastic filters, etc.
You must still supplement this with a ground rod or other electrode. Rods are most common. There is a minimum resistance rule to be met and testing is not easy so most simply install two rods (6' apart minimum).
The wire to the rods only can be #6. The wire to the water pipe must be #4.
I'm really not clear on your description of the bars in the new panel, but this is irrelevant. ALL neutral and ground bars get bonded to the panel box. Neither bar remains isolated. So if there is a bond strap/screw, use it.
Sometimes I feel like if I answer any more questions it is like someone trying to climb over a fence to jump off a bridge and me giving them a boost.