Microsoft .NET Core is a completely new thing in the Microsoft web stack when it was introduced. So before going to .NET Core some introduction of the history of .NET web stack is necessary.
ASP.NET Web forms
In 2009, Microsoft introduced a new framework for web development named ASP.NET MVC, which is based on Models, Views and Controllers patterns to keep a separation between business logic and presentation logic and allow complete control over HTML mark-up. For developers, it became easier to write code in ASP.NET MVC as compared to Web forms. It was so easy to write code as Models, handle the business logic in controllers and generate Views from controllers. Everything is controlled in ASP.NET MVC.
But ASP.NET MVC, although solving the problem of slow release cycle and removing HTML markup abstraction, still suffered from the dependency on .NET framework and System.Web which strictly made it coupled with IIS and windows.
ASP.NET Web API
This library was even more modular than libraries. It was developed by Windows Communication Foundation (WCF) team instead of ASP.NET team so it doesn’t rely on System.Web and IIS. This made this library completely independent from ASP.NET and IIS.
What will you Learn?
After learning ADO .NET start ASP .NET. Learn what it is, why it is used, what are the controls, what are ASP tags, what are attributes for a control etc.
1. Learn Grid View control, events in Grid View, its properties.
2. Learn MultiView Control
3. Learn Template and Bound fields
4. Learn about client side and server-side validation
5. Learn about view state, session state variables
6. Cache management in asp .net
7. Exception handling
8. Global.asax file
9. User defined controls which include User controls and custom controls
10. Master pages.
11. Action filters
12. Dependency injection
13. jQuery ajax
14. Targeting to mobile
Start to learn the front-end technologies like:
1. jQuery - to manipulate Html DOM
2. Angular /React- to build SPA applications
After that learn a back-end programming language (systems language):
Then at the end learn a language used to manipulate data in Database. I would suggest you learn:
Entity Framework (.Net framework to interact with data)