What version Visual Studio and Runtime is best to Use for .Net Core

Greetings,

        I started an internet project using MVC5.  I am now getting familiar with and trying out .Net Core features in VS205 Update 3.

        At this point we are trying to determine whether to upgrade out test web server with .Net Core bundle.  We have an up to date Windows server and would use IIS 8.5 and .Net Framework 4.5

         Is .Net Core stable for Production?  That will determine whether we should consider upgrading our test server.

         What version of Visual Studio is best to use for desktop development phase,  VS2015 Upgrade 3 or some version of VS2017.

Thank You