You can’t fault Paige Padgett for being slow on the uptake. The makeup artist hopped on the natural beauty train early despite professional challenges that came from incorporating alternatives to conventional products in her kit and has...

For Amazon, the world’s most gigantic e-tailer, large consumer goods companies and private-label lines move enormous quantities of merchandise, but budding beauty players took cuts of the action, too, on Prime Day, the biggest shopping event in its...