I would like to get some different perspectives on this.
We currently use SharePoint 2013. This was installed about 3 years ago by a vendor. I think it may have been their first install because we have seen several things that were not set up correctly. We have had some weird issues, anomalies and things not working correctly  from time to time. So my thought is rather than upgrade to 2016, we stand up a new farm on new servers for 2016. What are the pro’s and con’s?  What does this involve? Are there any third party tools that we could use to transfer content from  SharePoint 2013 to SharePoint 2016?
The best approach is to use the database-attach method to upgrade.
Before this, I would suggest you to do a test migration, try one or more trial upgrades. The goal of testing upgrade is to find and fix issues before the real upgrade. Here is an article to learn how to upgrade content databases from SharePoint 2013 to SharePoint Server 2016.
Another option is to try third party migration tool, like Lepide SharePoint migrator that provide pre-migration analysis to analyze and migrate.
Hope this helps!
