The most awful museums are in China. They have magnificent stuff on display and just the worst way of displaying it. They just don't spend money on lighting and installation.
I don't really have a favorite camera. I use a Leica and Canon a lot. It depends, especially professionally, on the requirements. But my carry-around camera is a Leica.
Covering a historic event is perfectly legitimate. It's not sneaking into somebody's boudoir... These people belong to history, and not to record that if you have the opportunity would be wrong.
The thing is that when you don't carry a camera, that's when you see pictures in particular, or at least that's when you think you see pictures in particular. When you do carry it, if you do see one...
It's almost embarrassing, but I do have one trick for taking portraits on commission. I carry one of these little bicycle horns in my pocket, and once in a while, when someone is sour-faced or stiff,...