OK. We have to find out what the optimal height of your camera over the coin is. Yours is a long-zoom camera, whose minimum focusing distance is 100mm/4" in Macro mode. That's as close as you can get to a coin, and only then if you're zoomed all the way out. All the zoom does is effectively convince the camera sensor that it's closer to the subject, so as you zoom in you're "closer" to the coin regardless of how far away the camera is.
Your camera has a particularly long focusing distance at maximum zoom - if you're zoomed all the way in, you have to be 2m from what you're focusing on. So, I'm guessing the sweet spot for you will be more "zoomed all/almost all of the way out". The reason this is a factor is, the farther away you can get from the coin, the easier your lighting will be to do right. If you can get lighting you like on a coin at a distance of 100mm, by all means use it that way. If not, you're going to gradually - step by step - physically move the camera farther away, while also zooming in a little bit, until you can find a compromise you like.
If this sounds labor-intensive, you're seeing things correctly. You're making this camera do something it wasn't really made for.
It may be best for you to start close to the coin (let's call it 125mm just to be safe, zoomed all the way out) and accept what lighting you can bring, while you learn your camera's manual functions. And you're going to need to learn those functions to get best results.
For the moment don't worry about the final image size. Set it for the largest/finest possible image, of course. For your camera, that will be 2048x1536; it has a "larger" setting but that's all in-camera - it arbitrarily adds pixels to get the larger size and that will do nothing but screw up your shot.
For now, use Auto exposure mode, Auto white balance, Spot metering and consider using the timed shutter. In your case, that's only a 10-second delay (most cameras have 2 seconds also) so the wait will be a pain but it will eliminate the possibility of your hands introducing shake. You may not need to worry about that; some of us drink less coffee than I do.

All we want right now is to get a nice sharp focus. We'll work on the rest later.