How to you identify which integration to choose when you get a requirement

What is the approach?

Here is what I think you should consider while choosing the integration system. It hold good for both inbound and outbound.

When you get the requirement, first see if there are any Packaged Connectors (Delivered) for the third party directly with a little tweaks can help achieve the need.

Then if you were not able to find any delivered packaged connectors, try to see if there are any Core Connectors which are template based can help achieve the need of integration.

If you do not find one from above, check if you can do it with a custom report and through Enterprise Interface Builder.
And if any of the above does not show way for your integration needs, then you look out for Workday Studio. 

This is the final place where you achieve any complex integrations.

Summary:

Packaged connectors            - Delivered by Workday to connect with third party
Core Connectors                  - Template based.
Enterprise Interface Builder - Custom Report or Web Service
Workday Studio                    - Multiple output files, Read from different sources , Exceptions,                                                                                                   Inbound & Outbound in same integration.