Not able to select a disk to reinstall OS in safe mode
When the drive isn't selectable, you almost always will want to choose Disk Utility and erase that volume.

Once it's totally erased, then run a repair operation to be sure the basic structure is good. Of course, you lose all data to do this erase, so be certain your backup isn't connected and is verified.

If the installer continues to fail, then you either have:


Wrong disk format entirely - post what diskutil list or disk utility shows for all the specifics of the volume format (APM/GPT) and the filesystem details (HFS / APFS / which flavor of the previous or some other like ext/fat)
A faulty installer 
Some faulty hardware