Here are a few things I learned when upgrading my Ghost server. I tried first simply installing with the instructions provided on ghosts site. I started troubleshooting, and it went downhill fast, so I restored the server from backup so I could get a clean start.
I found that the problem was that I didn't upgrade the node.js version first.
Make sure you have the latest supported node.js version (which is 4.5.0).
To upgrade to a supported node.js version, run the following commands (ln command used here is for Ubuntu - You will have to tweak the path for your OS if different):
npm cache clean -f npm install -g n n 4.5.0 ln -sf /usr/local/n/versions/node/4.5.0/bin/node /usr/bin/node
Check your node version to make sure it's correct.
After that, you can follow the instructions provided. Be sure to back up using the procedures they provide. I had a full DigitalOcean backup which proved helpful in this instance.
 27 June 2017 - I submitted a suggested edit to the Ghost blog. We'll see if they'll accept it or do their own edit to include checking the node.js version prior to attempting an upgrade.