How to recover the OS on my iMac

First you should review this doc Mac startup key combinations and drill down on the Command (⌘)-R links to make sure you can use Internet recovery. Depending on the OS-X/MacOS version your system has you may not have it.

Here’s a good reference on the different recovery options:

• How to Re-Install OS X with Internet Recovery on a Mac
• How to Restore a Mac from a Time Machine Backup

So basically, you can leverage the OS which is on your TimeMachine backup or use Internet Recovery. If your internet connection is not very fast I would recommend using the TimeMachine method. To make things easier next time I would recommend spending the effort to create a OS installer USB thumb drive following this guide How to create a bootable macOS Sierra installer drive. I do recommend you stick with Sierra as the highest version of MacOS as High Sierra has issues with SATA based SSD’s as the installer will upgrade the file system to APFS which has issues with SATA based drives and is not compatible with HFS+ volumes.