Ok, that is an early or mid 2009 iMac, so pretty old. Came originally installed with El Capitan (OS X 10.11.6). Just to be sure, pressing the Option key needs to be held down until the various boot options appear. If you don't do that and if the Recovery partition is the only one on the drive, that is what it will boot into. From your description, that is apparently what is happening. Are you holding down the Option key from power on until you see the options? Ditto for getting into Internet Recovery, you have to hold down the keys until you see that it is asking for login data for your network to get to the Internet. If you are consistently NOT getting to the various devices either they are NOT bootable or you aren't holding down the key(s) long enough.