I have done some further reading and it does look like if you need/want a desktop application- OneNote 2016 is the best option, as it does not appear there is a OneNote 2019 desktop application. Only the Win 10 OneNote Application and Office 2019 will install/default to windows option.
That being said, @IainB, my questions arise from the understanding that Microsoft has already made the decision to make OneNote an online driven application moving forward. It is possible that my understanding is incorrect but I do not believe that is the case. It is also possible that Microsoft might backstep the decision to make OneNote a web app, or that they will roll out some new enterprise OneNote version. From my vantage point, much of what MS decides depends on the revenue stream and or their tring to "win" over market share. I do not think OneNote's market is solely business. I think they are going after the evernote market, which has its fair number of business persons, most of whom have cast aside concerns for privacy or believe that encryption/passwords are enough. Evernote and other similar products want to sell online storage. Microsoft might be looking to do the same, or looking to use OneNote to help attract people to utilize their other products. In the past Microsoft has been slow to adopt the service model. They now push 365 pretty hard, and I have read some articles that mention them moving to a similar model for their operating system itself.
Back to my understanding of where OneNote is right now. Microsoft has made the move to stop developing/updating OneNote 2016, and instead is only developing the Windows 10 OneNote web app
which (as I understand it) requires a login to the web, and only allows working offline through caching. All files are born online. It is a web app that allows for use offline. When browsing Microsoft's forums about this move, people are encouraged to express their opnions through the uservoice channels with the hopes that Microsoft might reverse their decision.
OneNote 2016 will have some updates until 2020 and security updates until 2025 which is nice. That being said it would be nice to see some of the advancements from the webapp in 2016. For one, it would be nice to see better hand writing recognition.
One of my other concerns was my move from Win 7 to Windows 10. I had read a number of people complaining that Windows 10 would cripple their install of OneNote 2016. I found this concerning. I would be interested in knowing if anyone here has had issues with that. I have installed OneNote 2016 on a Windows 10 computer and it seems like both OneNote 2016 and Window's own OneNote are coexisting fine, but I have not tested it thoroughly. I would be interested in hearing from people here if they have had any issues.