If you are planning to build API and make them available as micro services and your code assets are C#/.NET Framework/Windows then you have some choices :
ASP.NET Core comes with an internal web server called Kestrel : kestrel claims to be a light and fast web framework which runs ASP.NET Core applications without the need for IIS in front (you might decide that IIS is usefull for other things). Kestrel allows for middleware modules (like IIS ISAPI filters) that allow for adding features to the basic server.
Katana (OWIN Microsoft implementation) is a collection of NuGET packages for building OWIN applications.
Plain old IIS + ASP.NET REST API code
Some good information can be found here from uShip guys
I’m basically writing this for myself as a reminder for the new .NET Core Microsoft environment.