>>>Just can't quite get my first test project to go away...
>>
>>For solns and projcts, right click it in the properties pane and you will see remove item in the context menu.
>
>I am right-clicking everywhere and I do not see a remove option...

Are you right-clicking a project or a solution?
If you right-click a project you should see Remove in the context menu. Selecting this option will remove the project from the solution, but the files will still remain on disk (to remove the files you have to use the explorer)

Deleting or removing a solution from withing VS does not make sense (IMHO).