Everything should be grounded to a solid ground, it doesn't matter where if its a good ground. Grounding the inverter to the battery terminal is redundant, it doesn't hurt to do it there, but it doesn't matter.
I would also give your display a good ground, as well as anything else powered for that matter. When I first cobbled everything into my truck to test some things out, I realized my entire system (PC, display, power) was grounded through the cable going to my headunit AUX-in. Don't even ask how this came about...can you imagine the ground loop I was getting? It sounded like a turbo.