Go for the Education versions, as these are mostly akin to the Enterprise versions of Windows 10. N is, as far as I know, a version that has some built-in Windows multi-media options removed. European legislation is to thank for that. If you don't care or use your own set of multi-media software, instead of the ones provided by Microsoft, get the N version.
You can use Education versions as long as you are registered as a student at an institution that Microsoft acknowledges as a school/university. Although I don't think they actively check on that. Depends also in which part of the world you live.Wikipedia link
to an overview of Windows 10 versions and their capabilities. That should give you an idea which version to choose.
Windows 10 build 1809 looks to be the more stable one. People migrating from build 18xx to 1903 have reported many problematic errors. Maybe a complete fresh install using build 1903 fares better, but I'm not sure of that. Usually a fresh Windows 10 install works better than migrating from one build to a newer build. Also, you can expect even more problems when you would migrate from build 17xx to 1903.
But as you want to keep as much as possible from your Windows 8.1 installation, you limit yourself to the migration option. A plain Windows 8.1 installation is not likely to give you a lot of problems during the migration to Windows 10, but you can expect migration problems, especially when using older/specific software or hardware (drivers).
If possible, create a Virtual Machine and install a trial version of Windows 10 (same build as you are going to get from your university). Then try if the software you depend on works inside this virtual machine. I remember you are using some very specific (and older) software. If that software remains working to your satisfaction, then go through the motions of migrating your computer and discard the Virtual Machine you created.
But if your software isn't working, then keep using Windows 8.1 until Microsoft drops support for it officially and see what you can do about getting a newer version of your software that does work with Windows 10. Or go and find an alternative for your special software, see if that works and migrate to that alternative software on Windows 10.
There used to be a tool, hosted by Microsoft, that could make an educated "guess" if your current hardware supports Windows 10 or not. But I think that was for Windows 10 builds 15xx. For all intents and purposes Windows 10 build 15xx isn't officially supported by Microsoft anymore. Even builds 16xx are out of support (with the exempt of LTSB version of Windows 10, if I remember correctly).
Understand that there are big differences between Windows 10 builds, so if your software works with one build, it is not a given that it will remain working in the next Windows 10 build. Enterprise versions of Windows 10 allow you to postpone migrations from one Windows 10 build to a new build for 1 year maximum. Education versions of Windows 10 are in most respects the same as Enterprise versions of Windows 10, so I assume that you have the same option to postpone.
It comes down to the ability of your special software to work on Windows 10, to see if migrating your computer to Windows 10 is a good idea or not.