Transfers through China, especially Guangzhou

I travel on a UK passport. My wife travels on a Taiwan passport. We live in the UK, but travel to Taiwan to visit friends and family.

What kinds of visas or travel documents do we need for transferring through mainland China airports on our way to and from Taiwan?

We've been told I need no transit papers, but my wife needs it, especially if we are passing through Guangzhou.

So, who needs what? How do we apply? What do we need to submit (pictures, etc)?

We'd be grateful if you could let us know what we need to do as soon as possible, as we will be travelling to Taiwan again in May.

Thanks.