I was not clear which object is checked out in your use case but grammatically, I think you were referring to the WTPart. Since the object does not need to be checked out to create a representation, I would think having it checked in would be the preferred option. Make sure things are stable when creating so that they are repeatable. When checked in, the WTPart is associated to a CAD object so therefore you have the 4 options which allow you put pull from the CAD data in creating its representation. There are many options on how you want that representation to be created using configuration specification rules.
When you have the WTPart checked out, there is no CAD document technically linked to it (until check in) so you get the option as if there was no CAD associated. If you just create a WTPart on its own and have it checked in, you will see the same options where you can upload something. Copy/paste a representation from CAD is also an option.
As far as the EPM Config and the other options when checked in, these typically are defaulted in the wvs.properties. Your main options are latest vs As-stored. I like as-stored since its static and can be recreated at a later time. Publishing rules can offer some additional files types to publish along with post-processing. You can also chose to publish as a position assembly which is key for very large assemblies that would choke the Cad worker,