You will need to do this by using the Automatic Questionnaire feature in the Lead Status. First, you need to designate your "New" lead status as your default status for any lead entered from a Contact Form submission. The first status in your lead tracking list (Settings > Workflows > Lead Tracking) will be your default status. You can re-order your statuses by clicking the Order button.
Next, click on your "New" lead status to modify its settings. Under "When a lead enters this status, automatically send:", choose Questionnaire and then a specific questionnaire template
Finally, define which shoot type should receive your selected questionnaire.
Now, when a lead enters this status for your specified shoot type, an automatic questionnaire will be sent. Visit this article to learn more about the Lead Statuses.