Our build server (TeamCity) does not have VS installed.

I can actually tell you the exact software installed on the build server:

  1.) Window Server 2016 (Base OS)
  2.) SQL Server 2016 Express with LocalDB only (used for longer integration tests that need to validate migrations)
  3.) DotNetCore.1.0.1-SDK.1.0.0.Preview2-003133-x64.exe (.NET core SDK 1.0.1 download from https://www.microsoft.com/net/download)
  4.) BuildTools_Full.exe ("Microsoft Build Tools 2015 Update 3" https://www.visualstudio.com/downloads/#d-build-tools).  If you have this, then you don't need the full VS install
  5.) NodeJs (for running webpack as part of 'dotnet publish')
  6.) TeamCity and Octopus Deploy agents

That's it.