Content type to Drupal commerce
I recommend making a sandbox install of Commerce Kickstart to see how they set up "Product display node" and "Product entities" to work together. Your "Training" content type would be the Product display node, and each course offering would be the product. To replicate this on your existing site, the high-level approach (you will need to sort details) is this:


Install Commerce and create references from Commerce product entities to your Training content type
Create some products that represent your courses. You can add custom fields where needed.
Display the products that are referenced to the Training nodes using Views module or methods similar to those used in Commerce Kickstart
This should give you a list of courses on each Training node that can be added to Commerce cart.