Sautéing mushrooms

I went to my parents house this weekend and we had steak and mushrooms for supper. My mother doesn't eat mushrooms, but is the one who prepared them. A few things I noticed she did made them turn out quite underwhelming.

First she sliced some baby bellas before washing them. That made them absorb a lot of the water when washing them in a colander. Then she used too small of a pan, so they were stacked and not all making contact with the pan. She also used too much butter and had green onions and minced garlic (from a jar) to cook from the start. They ended up boiling more than sautéing because of how much liquid there was. This did not actually allow the flavor of the mushrooms themselves develop, and made them still spongy and chewy. Then she added some wine (not sure what type, but it was too sweet).

I decided to coach her for future reference, and I was wondering if anyone else has further tips than these on how they do theirs.

First was to clean them with a damp cloth before slicing, then to put in about a tablespoon of butter instead of half a stick. I also told her to use a bigger pan so they are spread out and cooking from direct contact, then to add minced onions and fresh pressed garlic after they begin cooking a bit. When they are cooked to the right texture, then add cracked black pepper, a dash of salt, some Worcestershire sauce and a splash of red wine (preferably merlot). Let that simmer for about 15 or so minutes and enjoy.

Does this sound good? Any suggestions, tips, or other things you do? After having such disappointing mushrooms to compliment a beautiful ribeye, I'd like to make sure my next batch comes out perfect.