Quite simply - for 2003 - 2010, the administrative templates have made these very easy.
On 2013 - after getting the new ADMX/ADML sorted, I did easily find and disable the email signatures piece (ours is managed elsewhere).
However - Whether it was provided by Microsoft, or created by the previous admin, we had a convenient ADM template for turning off the ability to modify default stationary, Modify Default Theme and New Mail Using -> More Stationery
This covered all the bases so emails don't go around with pink backgrounds etc.
Am I restricted to creating a new custom admx template to sort this for 2013? I suppose I could review the older ones and try to mimic with 2013 in registry and then create the new template but that seems like quite a lot. If that's the only way though - I'm happy to do it. Just figured I'd check here first!
Thanks!