For some reason, when I press render and I have my output folder set, it doesn't render it there. How can I save my image to the output folder?
This is to be expected. Blender doesn't render the images to the output folder by default. This is only used when you press the render animation button.
One thing you can do to output your image, is to press F3 in the UV Image editor, and you'll get a promt to save the image. Sadly, it won't automatically save it to your output folder.
Another workaround, is to set the beginning and end frames to 1, and then press the render animation button. In that case, you'll get it rendered out to the folder you specified.