I have read about the difference between .NET Standard and .NET Core, but I really don\'t know what the difference is, or when to choose a .NET Standard library project and
Did you mean .NET Framework? Because .NET standard is an implementations, such as .NET Framework, .NET Core and Xamarin.
I love .NET Core because we can host it on Linux (use nginx in my experience). It's different than .NET framework which is you can only host on IIS. You can consider about hosting budget in this case (Because windows server is expensive for me).
In the development environment perspective, .Net core is lightweight. So, you can use VSCode, Sublime, for IDE (not only visual studio).