Get you best practices hat on, it's time to learn what you've been doing wrong. The internet can be a confusing place, but you can always come back to this guide to find out which file type is called for.
As far as I'm concerned, GIFs (which we all know how to pronounce) should only be used when you need a moving image, an icon, or are super strapped for space and speed. JPEG and PNG are less easy to decipher. The takeaway there seems to be that if you need transparency or don't care about space at all, go ahead and use PNG.
And if you have been using a PNG when all you needed was a JPEG, don't feel bad, I mean, who even knew that JPEG stood for something?