What if I don't have a new iPhone, but want to back-up / restore my current iPhone. Anything need to be done differently versus the purchase of a new iPhone?

You should ALWAYS be backing up your iPhone regularly (I'd recommend daily), whether or not you're planning on getting a new phone. The whole point of a backup is that in case the unforeseen happens (your phone gets lost, stolen, run over by a bus, dropped in the ocean), your data is recoverable.

Start here:

How to back up your iPhone, iPad, and iPod touch - Apple Support

Are you saying that you are not backing up your current phone? If yes......click the link below:

How to back up your iPhone, iPad, and iPod touch - Apple Support