Trouble upgrading iOS and iTunes

I have an iPhone 6 using iOS 9.3.5 (13G36). 27 GB available. I am trying to upgrade to iOS11.

When upgrading through the phone, after I click the 'download and install' I get a spinning circle and the process does not progress. I let it work overnight; 8+hours.

When I try to upgrade via iTunes I get the message "A new iPhone software version (11.4) is available, but you need to install OS X 10.10.5 (or later) and iTunes 12.7.3."

The info from the 'About this Mac' is:

OS X version 10.9.5.

2.4 GHz intel core 2 Duo

4 GB 1067 MHz DDR3

When I click the 'Software Update...' button I get to the App Store and the info there states:

Mac OS High Sierra (no updates available)

Updated June 1, 2018

Version 10.13.5

I am currently running iTunes version 12.6.2.20. I am not given an option to update iTunes.

Help is appreciated.

Thanks,

Dave