iMac OS X Mavericks No disk to select

You need to launch Disk Utility and erase the physical drive to format it as GUID partition and MacOS Extended (Journaled) before Mavericks will see a valid destination volume. I would actually click on the "Partition" tab and select "1 Partition" as MacOS Extended (Journaled). Then go back to the "Reinstall OSX" option. Mavericks doesn't know anything about the APFS file system (or possibly the newer CoreStorage).

If Mavericks won't finish installing or boot correctly, then you may have a failing hard drive.

Edit: Failing drive is likely if entering local Recovery Mode using Command + R booted you to Mavericks since this means the internal drive no longer has a bootable recovery partition and the system booted into Internet Recovery Mode. You can try booting directly into Internet Recovery Mode using Command + Option + R to install the latest supported OS.

Try this. You need to establish an Internet connection, preferably Ethernet or fast Wi-Fi.

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-Shift-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 tab in Disk Utility's main window. 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.

If the disk still does not show up, then it has died. BTW, if your internal disk is an HDD of Fusion Drive, then do not use APFS. The above procedure will install the version of macOS that was pre-installed when it was new.

Oh goodness gracious !! Usually you can't go back, eg, if you had Mojave, you can't install Mavericks on top of it. That being said, you should be able to accesss Disk Utility from the Mavericks install. You might have to move the mouse to the top center of the screen, and maybe OS X Tools might show up. First off, you might want to reset the SMC/PMU and zap pram on your iMac. Both things are simple enough to do. You can either check Apple's support page for Desktop computers, or if you can't wait, like me, google, or yahoo should get you that info. How in the world did you get OS X Mavericks ?? If you start up your iMac, with the option key held down, it will show you all bootable hard drives. I don't think Apple uses AFPS anymore. If you can, start up from the recovery partition and run Disk Utility from there. erase and reformat the hard drive as MacOSJournaled, and GUID on, and then try to reinstall the OS. During the OS X Mavericks install, you should be able to move the mouse up to the top left of the screen, and something should show up. Otherwise I suspect that the iMac's hard drive has been formatted improperly beforehand.

good luck, and keep posting here: someone will for sure help you out

jb