Hi Seth,
Thank you for writing in, that is actually a wise thing to do and the thing we would advise when jumping from outdated version to another.
What you can do is duplicate the live site on a developmental server and do the updating there first. This way your live site will be keep untouch, while you do the updating on the developmental server. Since this is a major update, it is understandable that few things will need adjustment/fixing, if you are not comfortable doing this, please hire a developer to help you on this.
- How to duplicate a WordPress Site
- Updating WordPress
- Updating Your Themes and Plugins
- Latest Version Compatibility
If you have any caching and/or optimizer feature (plugin, server-side, CDN) on your site, please clear and deactivate those on developmental site.
Cheers!