we want to create a rudimentary dashboard for a client in Jira. Only certain items like epics and defects should be displayed.
The question here:
only epics and defects should be displayed in the overview
Shouldn't be a problem. Create a filter that selects only epics and defects and then use the filter results gadget on the dashboard. Or two separate filters if you want them displayed separately.
when creating a new epic, we want to be able to select different types (similar to a ticket that can also be selected as story, defect, change request, etc.)
I'm afraid this will require administrator privileges. You will need to create a custom field and add it to epics.