New Camera

That Fuji seems like it might be a decent player in the Macro world. I've never played with one, but reviews tend to praise its' Macro mode.

I can't give you a specific group of settings that will work with your camera. There is no "one size fits all" setting for taking coin pictures. Different coins shot with the same camera will need different settings. What I'd advise is this: Start with it on fully automatic. Don't worry about anything but getting a clearly-focused image that's bright enough and big enough for your purposes. Do this by varying the distance from the camera to the coin, and how much light you put on it.

Like all zoom cameras, the more you zoom in, the farther away from the coin you'll have to be. Every camera has a minimum distance at which it can focus; what you're doing with the zoom is fooling the camera into thinking it's closer to the object than it actually is.

The Fuji has one funny quirk. Like most cameras, it has a round 4-way selector on the back - you push it at the 4 corners of the compass to make various menu setting changes. However, most cameras have a center button in the middle of that which confirms/chooses the setting; your Fuji requires you to push the shutter button halfway to confirm the setting, instead of a center button..