If you would like to include an email signature in outbound email, there are a couple approaches you can take. You can update your email template(s) used with E2CP to ensure a standardized signature is always included or make the signature optional by providing a canned comment that users can opt to insert on the New Comment page.
Approach 1: Update the email template(s) used with E2CP to include merge fields. This approach ensures that a consistent signature is included in every outbound email and that signature is not included in the body of the case comment.
Approach 2: Create a canned comment with "Current User" merge fields. On the Canned Comment edit screen, in the field picker, you will see fields prefixed with CurrentUser. End user can elect to include this and it will appear in the case comment body.
If you need to add a company logo, please refer to the following Salesforce articles:
Add Images to Email Templates in Salesforce Classic
Learn how to upload images for 'HTML (using Classic Letterhead)' email templates
Note: By default, we disable Salesforce's inclusion of the signature set up in My Email Settings because its appended to the extreme bottom of every outgoing email, rather than below the text of the last reply. For more information on this Salesforce platform issue, see: https://success.salesforce.com/ideaView?id=08730000000BqAkAAK