I cannot get out of recovery mode (OS X Utilities) by resetting or reinstalling the OS
On an 08 iMac, your options will be limited if the previous owner didn't correctly run through the reset procedure, leaving you with a nice, simple sign-in to take over the Mac as your own.  

Part of the procedure is for them to sign in on their own existing App Store account &amp; reinstall a clean OS that they are already associated with, as 'purchaser'. if they exit the process after install but before sign-in, then it's ready to transfer ownership.
Without that, you're left with trying to sign in as a new user with no previous purchase history &amp; no access to anything other than the very latest macOS - not good if your machine can't run that.

Additionally, an 08 is not capable of running Internet Recovery, so automatic access to the correct installer is not possible.

Theoretically, you could boot an 08 from USB, but in practise I've never managed to achieve that, earliest I've managed to do that on was an 09.
This may leave you with only an install CD as your working method, although it's always worth trying to get a USB key to work first.  

You are going to have to access the installer from another computer &amp; burn/flash your startup medium from there.