OP, are you picky about brands on these things: "I was thinking I'd mostly be buying paper/cleaning products/personal care items. Things like toilet paper, paper towels, laundry detergent, dish soap, Clorox wipes, windex, trash bags, toothpaste, tampons, shampoo/body wash."
They tend to have a limited selection as to brands. As someone else said, you need to check it out to see if they sell what you would buy.
I have found that the following items at Sam's Club are better than what I can get anywhere else in town: rotisserie chicken, corn bread, grapes, small size tomatoes (grape and cherry), white cake with white buttercream frosting, and "banker boxes." By "better" I mean taste, freshness and quality, not price.