you can save jpg images directly from photoshop and choose the quality (and thus size) of your image
lower file size will almost always result in lower quality (especially when you want to make it dramatically lower)
when you have square images, there's really no need to use png, just use jpg if you're concerned about file size
if you have transparency and need your image in png, google tinypng
you probably don't want to resize gif images if you're still worried about detail... those generally lose quality quickly, but you can always try