Thanks for your posting. TestRail automatically remembers the project and issue type selection per TestRail project and user for the defect integration. We are also happy to look into the option of configuring a default JIRA project per TestRail project. If you configure the integration per project (instead of globally under Administration > Integration), you can change the layout and fields of the Push Defect dialog per TestRail project and this is the recommended way to implement such kind of customizations. You can configure the per-project integration when you edit the project under Administration > Projects in TestRail.
I hope this helps!