How do I decide on a proper PCB ground layout?
I think via stitching is only needed if you're doing RF design. That said, the type of ground plane that is needed really depends on what circuit you are designing. If you have high frequency, switching signals, then you will want a uniform ground plane with short via traces attached to your components. If your PCB just uses discrete components with analog signals, then I think what you have in your first picture is okay.