This is exactly what you’ve already chosen (Web Application).
Basically, you can choose that option and get an ASP.NET project with templates or choose ‘Empty’ which equivalent to ‘ASP.NET Empty Web Application’. This option gives you an ASP.NET application without any template.
About the second question, you can fine some details here.
Basically the main improvement, in VS2015, is that Microsoft has added a lot of components in order to enable mobile development via VS2015. Now, with VS2015 you can develop application for mobile like Android based system, IOS etc… Just like we could do by Android Studio.
Additionally, with VS2015 we can develop cross platform applications for Mac OS, Linux, etc…
If you are going to do so, consider installing “Visual Studio Code” on your target machine.