PNG is useful when you need transparency or lossless image storage. JPG is usually more convenient when the image is photographic and a smaller file is preferred. Converting PNG to JPG removes transparency, so transparent areas need a background color.
For photographs, JPG quality around the high or medium-high range is often a practical starting point. After conversion, compare the result at the size where it will actually be used. A very high quality setting can keep files unnecessarily large, while an aggressive setting can create visible artifacts around text and edges.
For websites, smaller images can improve page loading, but the correct format depends on the image and browser support. Keep an original PNG if you may need transparency later.