Need help upgrading my Project

Hello,

I started a WEB API project with Visual Studio 2015 last year in June 2015. Since then the project has grown to be pretty massive and is currently being used in production serving clients. The biggest fear I currently have about the project is the fact that it is becoming out of date and we are having a difficult time upgrading the dependencies, and adding new "WCF Services" (SOAP APIs).

The biggest issue with upgrading is confusion on what is the greatest and latest framework to use. In addition, with our "telerik", "force" and "chargify" dependencies being essential for our business we want to upgrade without breaking them. When using .net core the don't seem to work with the project because they are dependent on .net. 

This is our "project.json" file.

{"webroot": "wwwroot","version": "1.0.0-*","dependencies": {"Microsoft.AspNet.Mvc": "6.0.0-beta5","Microsoft.AspNet.Server.IIS": "1.0.0-beta5","Microsoft.AspNet.Server.WebListener": "1.0.0-beta5","Microsoft.AspNet.StaticFiles": "1.0.0-beta5","System.Data.SqlClient": "4.0.0-beta-22816","System.IO.FileSystem": "4.0.0-beta-22816","System.ServiceModel": "1.0.0","Microsoft.Net.Http": "2.2.29","telerik.reporting": "9.2.15.1105","DeveloperForce.Force": "1.3.0","chargify": "1.1.5967.40624"
  },"commands": {"web": "Microsoft.AspNet.Hosting --server Microsoft.AspNet.Server.WebListener --server.urls http://localhost:5000"
  },"frameworks": {"dnx451": {"frameworkAssemblies": {"System.Runtime.Serialization": "4.0.0.0","System.ServiceModel": "4.0.0.0"
      }
    }
  },"exclude": ["wwwroot","node_modules","bower_components"
  ],"publishExclude": ["node_modules","bower_components","**.xproj","**.user","**.vspscc"
  ]
}

I would greatly appreciate any help/guidance on what to do with our project at this point. With all the new Microsoft tech coming out of beta we would like to be on the right path for long term support. 

Thank You!