what focusing mode should I use

Any AF mode that works for you is fine, but many people prefer to set the camera to manual focus mode and make fine adjustments to focus by moving the camera. You can mount the camera to a macro focus rail and mount that on a tripod to make it easy to make and maintain small front/back and side to side adjustments.

Matrix, Spot or what?

Those are metering modes. Again, anything that works for you is fine. That said, it's easy for the light meter and auto exposure system to be fooled when doing macro work. For example, filling the frame with a white flower can cause the camera to think the scene will be overexposed and try to compensate, giving you an image that may be much darker than what you want. For that reason, it's a good idea to work in manual exposure mode and adjust the exposure parameters (shutter speed, aperture, ISO, flash) yourself to get the shot you want.

I would like to take photos of flowers, leaves etc. that fill the whole image and are sharp basically right across the photo, rather than just in one dedicated spot.

That's a depth of field problem more than a focus problem. When the subject is very close to the camera, you get very narrow depth of field and it can be hard to get everything in focus at once. Using a small aperture helps, but you may need to add light to the scene (via speedlights, for example) to get the exposure you want.

The problem is compounded if you're hand holding the camera, because very small movements can have a big impact on focus. In that case, you'll want to use a servo autofocus mode so that the camera is continually adjusting focus right up until you take the shot. Image stabilization will also help if it's available.