Check if package is compatible with .net core

I started programming with .NET Core and ASP.NET Core and after reading many Docs/Tutorials i still am not sure of how to realize if a Nuget-(Meta-)Package is comptabile/usable within my .NET-Core-App.

1. How to check if a NuGet-Package is compatible with .NET Core. E.g. the often recited Newtonsoft JSON. Is it compatible/usable - and how to see this?
2. Is there a list of all the available .NET Core packages?

(Like here it lists a few

key NuGet packages for .NET Core

). But since they say those are "key" packages i would assume there are more. But which?