I've tried really hard to solve this myself but I can't. :(...
I tried to modify my installation, but all that did was change the titles to make things even more confusing.
Have a look here.
What I should be looking at.
What I am really looking at.
As you can see there are differences. After reading the below answer in another thread...
"Ensure you have the Microsoft Web Development Tools installed which you can find in the Visual Studio installer under Windows and Web Development
Once installed, start up Visual Studio and check your templates again and you should see the ASP.NET Core templates.
For those who already had visual studio 2015+ installed but didn't add the feature during the inital installation, you have to download the main visual studio installer and modify its features"
Things only got stranger with the titles being changed from Class Library (.NET Core) to NetCoreClassLibrary and NetCoreConsoleApp.
I have also followed instructions here.
What happened in the lead up?
First, I got update 3. Then I got Microsoft .NET Core 1.0.1 VS 2015 Tooling Preview 2 and installed. After that I modified my install to make it like this, but after that failed I went back to recheck update 3 but machine said that it was still installed. Now I have no idea what to do.