After I mapped out the UV's I went to go put the texture on my model. I wanted to try layering the logo on a metallic background, but when I went into photoshop to remove part of the logo I realised the image wasn't as high quality as I wanted. I decided to look at images of yin-yang symbols and stars to piece together a new, higher quality logo from scratch. I then had to experiment with different fonts to find a match to the original image, which I somehow managed to do relatively quickly.
After this, I played around with making a metallic texture and playing around with the transparency. I managed to get a decent amount done, but once it came to adding more nodes and connecting things up I struggled without a middle mouse button. However, I think once I have access to a mouse I'll be able to add an image to the reflectivity so it's not so dark. Hopefully I'll be able to connect up everything else so I have a layered texture instead of a metal coin and a floating, transparent logo.