Ok thanks for your help, after a bit of work, I think I've worked out a good combination that works with DNN.
This might be useful for other new users...
Here is what I have in my Web.config:

... 

EditorBodyStyle="background-color: #FFF; color: #000;"
EditorWysiwygModeCss="~\Portals\_default\Skins\SKINNAME\skin.css"
...

You should point your EditorWysiwygModeCss to your skin.css file.  This is because if you point it to another CSS file, those styles are not going to be applied to the page when you update the module - i.e. any other CSS file would only be applied whilst editing, whereas the skin.css file is always applied to your pages. 

You could if you want set it to another CSS file, as long as the styles defined in it are the same named styles that are in your skin.css file.  You could do this for example if you only want the user to see a subset of the styles defined in you skin.css.

Also, I would not style HTML tags directly in your skin.css file - for example I was styling the p tag as follows:

p {
  color: #FFF;
}

This causes a problem in the Cute editor, because all the drop downs were showing white on white, so I couldn't read what any of the styles were called when editing.  

I tried to fix this by adding color: #000; to the .CuteEditorDropDown styles in the 'Themes/Office2003_BlueTheme/style.css.aspx' file.  This made the text in the drop downs black on white, but had the undesired effect of not showing what the true colours of any styles I had defined in skin.css were.

I hope that helps someone!