You could do this pretty easily in Rules with the following logic.
- After completing Checkout process
- 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
- 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.