We work with TFS 2015 and it works really great. We have two different build sets one for our production environment and one for our test environment. We also use CI. Our current workflow is that we "Queue build..." and then everything is done automatically. What we would like to accomplish on our production build is one of the following:
Don't use builds for deployment. If you're on TFS 2015 RTM or Update 1, upgrade to TFS 2015 Update 2 (or, ideally, TFS 2017 Update 1). Starting in TFS 2015 Update 2, there is a Release hub that has exactly the kind of capabilities you're asking for. It allows you to define a release pipeline for the binaries generated by a build, where you can put optional approval requirements in place prior to a deployment occurring on a given environment.