Welcome to the forum
It would be best to ground everything to the same point, however that is done.
Also, if you haven't bought that inverter yet, I suggest you don't. Take a serious look at the Opus power supply, it is awesome, and will give you everything you need for a carputer installation, especially if you are as serious as it looks like you might be
I regret not getting an Opus straight off, but instead have been through the inverter, and Morex DC-DC routes, and have spent almost as much already as an Opus costs, and STILL don't have the best power setup. Hence, why i'm getting (and currently pimping) the Opus power supply