Entity Framework, MVC, ASP.NET, ASP.NET Core etc… etc

I'm looking to develop a basic website to administer a sports league. I'm an experienced SQL Server database developer but am new to web development. I wish to make full use of my database skills in manipulating data so will be preferring to use the efficiency of pre-compiled stored procedures for my CRUD operations (as opposed to the hard-coding a mass of "SELECT/UPDATE/DELETE...FROM...WHERE" statements within my web application. From what I see there are a maze of options for which technology I might choose for my web application and it's got my head spinning as to which way to go. My instincts tell me that an MVC application will suit my needs but that's where it all gets blurred. What's the difference between ASP.NET and ASP.NET Core? Why would I favour one over the other? To add to the confusion, I keep hearing about Entity Framework and Entity Framework Core: are these aimed at those developers who either prefer to not to get too involved in back-end stored procedure-writing or don't have the necessary skills to manage databases? Finally, am I missing something fundamental that I ought to be becoming familiar with before jumping in? Any help appreciated.