TeamCity comes with MSBuild so that you can build your solutions directly by selecting a runner type of MSBuild in the Build Step. You can also choose the version of Visual Studio your developers use and since TeamCity 8.1, Build Tools for 2013 are supported too.
However if you need to run MSTest for your unit tests TeamCity recommends you install the full Visual Studio. If you already have a licence for this then it is ok to install a second copy for your build server, but what if the build server is at a client premises and they don’t want to buy a license? I came across this stack overflow post that pointed me to an MSTest Agent download for 2010. You can download the Agents for Visual Studio 2013 from here. All you need is the executable so don’t install the agent as a service and you don’t need the controller.
Hope that helps.