You could do this pretty easily in Rules with the following logic.

Event
- After completing Checkout process

Condition
- Entity has field - commerce order line items have field commerce_product (this is how you access the product information in the Rule
- Data Comparison - Product Type is something

Action
- send mail

Create another rule afterwards for a different Product Type

You could also download Conditional Rules, https://www.drupal.org/project/rules_conditional, and use that to allow you to create only 1 Rule and setup a condition of If Product This, Do That, Or If This, Than That.