We are a mostly MS shop at work doing .NET LOB development. We also use MS Dynamics for our CRM app... all the devs are currently using VS/SQL Server 2008. We also use VSS, but
Comparing TeamCity to Visual Studio Team Services (the latest cloud-based offering from Microsoft):
Both work great for implementing a continuous integration process
TeamCity is more mature and everything just works.
Visual Studio Team Services by contrast is constantly evolving to catch up with TeamCity and some things just don't work well (e.g. try triggering builds based on paths that have changes from Git - the documentation is weak and the feature itself just doesn't work (as of August 2016))
Visual Studio Team Services makes it easy to have only cloud-based agents running your build (the downside however is that each has to do a clean pull of your repository for each build which may add a minute or more to the build). Both can also support local build agents which do not need to wipe the working directory for each fresh build.
But in either case I would highly recommend you also look at CakeBuild which moves most of the configuration information about how to do a build out of the CI system and into C# code that is in your Git repository along with all your other source code. With CakeBuild you can run the same build locally as you will run in the CI system and if you need to go back a month to build a specific version you have the source code and the build script to do it.
With CakeBuild in place you are now free to easily switch between TeamCity and Visual Studio Team Services.
The only downside to CakeBuild is that all your build steps are bundled into a single task in the CI system which makes reporting slightly less nice and may involve some extra work to get the test results out into a format that the CI reporting system can use.