How to make external drive my iMac Mojave startup

The SSD would be the better choice. If you need to do Internet Recovery then do this:

Internet/Network Recovery of El Capitan or Later on a Clean Disk

     If possible back up your files before proceeding.

1. Restart the computer. Immediately after the chime hold down the (Command-Option-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (will be the out-dented entry) from the side list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Install OS X and click on the Continue button.