I looked at the list of museum types along with their descriptions. I have to say that I can find something of interest in any of them.
Having said that, and keeping in mind that there are always exceptions, my least favorite kinds of museums are those that feature military history with tons of armor and weapons, and those that are the houses or castles of the rich and famous, glorifying conspicuous consumption. I'm not a big fan of Baroque or Rococo art or architecture, but I do like a few of the pieces of a few of the artists and musicians.
I've never felt the need to see it all in any large museum. Trying to see it all is exhausting, mostly because of the high level of visual input, no matter what the kind of museum.
I do love open air museums that show the living history of the time they are portraying. An early European favorite of mine was one in Denmark. I forget the name, but every house or shed or barn was represented with suitable tools or clothes or decor. But, there was always an anachronism of some sort. Examples I particularly remember are an electric percolator in a 16th or 17th century kitchen area and an electric circular saw in a workshop of the same era. Some exhibit designer had a sense of humor.
A more recent favorite is the Museum of Cycladic Art in Athens. For me it's the perfect size and the perfect blend of art, history and culture.
Museums or art or music that encourage me to think and learn and move me tears are rare. The United States Holocaust Memorial Museum in DC is one of those. I visited it in the early 1990's, not very long after it opened and I still think about what I saw and learned and felt there.
I have a similar experience when I see Picasso's Guernica. I wish the Reina Sofia in Madrid had a way to study it, not just see it.