Forget the VGA input. Why would you want the video from your Mac mini to have to go through a digital>analogue>digital conversion? Keep it pure digital all the way with a DVI>HDMI cable.
FWIW, I'm using a 2009 mini in full 1080p with the previous-generation Panasonic 42" plasma, and it works like a charm. All I needed to do to ensure that the desktop filled the screen properly was to have overscan switched off on the TV, but on on the Mac. I would imagine that the current-gen Panasonics are the same.