PNG is lossless, so it will look exactly as you made it. But JPG is useful for files like photos (and planetary textures), if you need them to be smaller. If there are many areas with a single color, PNG is better though, as JPG will make strange patterns in them.
JPG also get's worse every time you edit it and save it, so it's best to save an original as PNG, and copy it and make that one JPG when it has to be uploaded.