>If you were going to develop a new "responsive" web-site to handle mobile and browsers, what combination of packages would you use to do so? I'm coming from Silverlight, wpf, wcf, entity framework, etc.

I like angular/bootstrap on the client. If you haven't used it before then it might be best to start with angular 2.0 even though it's not complete yet.
If you go with angular 1.x then use the ui-router library rather than the standard router.
I see Craig wonders about performance on mobile but I've not found it a problem - if you're designing for mobile pages tend to be simpler and smaller.
I'd also suggest looking at TypeScript - it helps a lot with type safety and modularization (is that a word?)

Personally I use very little MVC on the server - don't like mixing the logic. Most pages are static HTML using WebApi/EF to supply data to angular.

Depending on the app you could consider using node.js on the server rather than asp.net and even a no-sql db like MongoDb