If you are having trouble getting the form to insert the way you want it to appear you can edit the shortcode directly to include the fields you want to have. If you want to add a required email field, and an optional comment field to the above shortcode you would change it to:
[contact-form][contact-field label='Name' type='name' required='1'/]
[contact-field label="Email" type="email" required="true" /]
[contact-field label="Comment" type="textarea" /][/contact-form]
Please let me know if that doesn't work for you.