I wrote some Windows services before with Visual Studio 2010, which provided the Visual Studio Setup Project. It had some quirks, but it worked for me. Starting with Visual Studio 2012, Microsoft did not include this project type anymore. Many complaints of the community followed, and in the end they built a VS extension, which brought back the old setup.
There is also (the better way) going with WiX installer (https://wix.codeplex.com), there is even a service template: https://visualstudiogallery.msdn.microsoft.com/7f35c8ce-1763-4340-b720-ab2d359009c5
In this post, however, I will use the new VS setup project extension.