Welcome to .NET on Linux! As you have noted, things are moving pretty quickly in this space. But I think we can get a stable environment without too much trouble.
Version alignment is critical. We'll want to make sure we have the same version of .NET, the examples, etc. in place. So I'd recommend working with Red Hat's .NET Core 1.0.
The Red Hat installation instructions (same link you provided) should work. (If they don't, start a discussion on just that problem. I'm sure it will get ironed out.)
Once Red Hat's version of .NET Core is up and running (it's easy to validate with 'dotnet new, dotnet restore, dotnet run') you can progress to some of the ASP.NET examples on GitHub-- but be sure to use the tag for 1.0, otherwise that alignment problem will arise!
I don't have much experience with Visual Studio and .NET Core 1.0 (I like to use VSCode), but I imagine Version alignment will help there, too. If Visual Studio gives problems, feel free to discuss that here, too. (Or even open a ticket if you are a Red Hat subscriber or Microsoft subscriber.)
These are early days for .NET on Linux, but things will pick up steam quickly. Did you notice the cartoon on DZone just today ?