Hello,
I have taken a look at your attached image and can definitely clean up the image background and enhance the image for you.
I am a photographer and retoucher - you can see samples of my work in my portfolio here.
In terms of the size and the quality, unless you have very particular requirements 300dpi is sufficient for printing. Printers and the human eye generally won't be able to discern more detail at regular viewing distances. The image can be scaled up to the A3 size you wish, but no new detail will be in there. However, I can enhance the image to improve clarity and bring out as much detail as possible for you.
Please don't hesitate to contact m to discuss this further your specific requirements.
Regards,
Nikaya