This is the bag that I currently carry. It fits under my arm nicely and doesn't slip to much. It has a black interior (sorry SCB) with a few small pockets and a zipper pouch inside.
Inside I carry- my reading glasses, my wallet, a makeup bag (that's new to me) my change purse, my keys, a pen, a paint swatch, anti bacterial wash, and a measuring tape. My sunglasses live in the car so I don't carry those in my bag. This set up makes it easy to change bags.
I do have a large waterproof type envelope bag that I carry my sons diapers (because he doen't want to be potty trained-that's a long story) wipes, extra pants, extra cup, disposable bags and a oatmeal bar. I don't carry that into stores or anything, it's just my emergency kit for the car. I have never owned or carried a "diaper bag" because he had never needed one , he has never had an "accident" before, not even as an infant. Was I lucky or what?