I am really curious about this! Please @ comment to me if anyone comes up with other/better ideas.
Option 1: ASP.NET Web project with Web Essentials
If you just want a front end javascript project, this is an easy option. Web Essentials is easy to use and install in Visual Studio. You can use this for easy minification. Then you can use Qunit for testing. This is a pretty easy and light weight entry point into javascript client-side development.
Option 2: Node.js Tools for Visual Studio
Use Node.js Tools for Visual Studio. It will give you project templates for a lot of these good things. You may not end up using node.js especially if you are just creating a client side js library, but having node.js is helpful for testing and you will want/need npm to install all the other good things mentioned in my original answer (Option 3).
There is a lot of setup involved with this one. It may be a barrier to entry for some .NET developers.
Option 3: Web Site Project
Here is what I have done in the past:

I actually created this project in Eclipse! (Don't hate me). Later I created a Visual Studio solution with a Web Site Project. I installed node.js which is certainly not required, but I was using it as a lightweight web server.
Then you can use Nuget or Bower to install other things like:
- require.js for module management
- jasmine for unit testing
- grunt or gulp for builds (minification)
- You could install jslint or jshint for code correction.
Not all of these things are required. I think Bower is integrated into Visual Studio 2015. Some of these will require command line builds, but there are very few commands to run once you set it up.