Create and load a custom view, like a table or a list, that shows what you want.
Create and load a type extension that defines a DefaultDisplayPropertySet. Only those properties will display by default.
These are usually easiest to do if the code that creates your custom object is in a module. You can use the module's manifest to also load the custom view and/or custom type extension as part of the module, so that it all happens transparently.
"PowerShell In Depth" covers all of this. You can also review the help for Update-FormatData and Update-TypeData, although they do not completely document the XML syntax. In the $pshome folder you will find the .ps1xml file (type extensions) and .format.ps1xml files (format views) that PowerShell ships with. I've used those as examples in the past.