Recs.
Updated
With ASP.NET Core you can build web apps, web services, IoT apps, and mobile backends. It can be used with Visual Studio, or with Visual Studio Code.
Read Getting Started With ASP.NET Core 5.0.
SpecsUpdate
Pros
Pro JSON API's
From .NET Core 2.1 new APIs have been added to write JSON APIs that require less memory, using Span<T> and UTF8 strings, and improve throughput of applications like Kestrel, ASP.NET Core web server. See also Utf8JsonReader.
Pro JSON optimization
In .NET Core 2.1 and 3.0, new APIs are added that make it possible to write JSON APIs that require less memory, using Span<T> and UTF8 strings, and improve throughput of applications like Kestrel, ASP.NET Core web server. See also Utf8JsonReader.
Pro Built in Dependency Injection
Where in the old ASP.NET we had to rely on 3rd-party solutions, Dependency Injection is now built in.
Read Implementing an Effective Architecture for ASP.NET Core Web API.