Your first question is SD or HD. My answer is HD. There are a few last bastions where you want SD.

For example your museum has some classic 4x3 SD displays so shooting in the native format is best.

Skipping over the product questions I see this question.
"prefer my discs to contain the full HD quality so i can watch them on my HDtv via blue ray player.

is this possible?"

Absolutely. Many players support you moving AVCHD files over. But doing so manually while possible (and not something I will discuss) I suggest you get an app for creating such. If you want to do this manually there are a lot of web pages about that.