I too, had an ancestor on the U.S.S. Minnesota. He enlisted in 1885 and you can see his entry here in the link below. It's from familysearch.org listed under United States, Naval Enlistment Rendezvous, 1855-1891. Perhaps others can find their ancestors here too. (be sure to scroll across the page...it's a spread)
https://familysearch.org/pal:/MM9.3.1/TH-1-14739-46946-17?cc...