Career advice as a ASP.NET web developer ?

Question

I am 33 years old and I have learned web forms with C# at faculty. Also I created more than 5 schools projects in Web Forms at the entry or beginner level. After graduation I have worked 3 years in industry not so well connected with software development. After that I was 6 years unemployed, because I was helping my family and I wasn't available for full time job. Meanwhile I have learned ASP.NET MVC and I have done one project where I have demonstrated the learned skills. I also know C/C++, Javascript, Xml, Ado.Net, Html and other it skills not related to the web development.
I don't have professional experience in web development and now I am looking for job and advice where should I proceed with my career as a ASP.NET web developer.

Should I improve my skills in ASP.NET MVC or should I start to learn ASP.NET CORE MVC?
What is your career advice for me?
Should I improve my skills with some new technologies on demand? Which technologies should I learn?