I would like to know if I am creating a subsite from a team site how I can edit the template to inherit the branding I apply to new subsites.
Is this possible and which template(s) do I edit.
You can reset the subsites to inherit the master page of the parent site in the masterpage option located under Settings -> Site Settings -> Look and Feel -> Master Page.
This option is disabled by default in the Team Sites to activate it you have first to activate the SharePoint Publishing features.
Note: The Team Sites in the SharePoint 2013 inherit the masterpage from the system sites.