There are two ways to delete "My First Board":
a) Not have it being created in the first place by specifying, when you create the Workspace, that this Workspace is a "Scrum" Workspace (see "advanced" option in the "new workspace" dialog box)
b) If "My First Board" is already there, then it's like the "default" board for the Workspace, hence you cannot delete it. Once you set your backlog board to be the "default board" (under "Workspace Settings", "Defaults"), you'll be able to delete "My First Board".
Hope this helps.
and good suggestion on supporting more than on "Backlog", we'll add this to our product backlog. The way our users do it now, is having a "backlog" or "To Do" board withing the Sprint board.
Let us know if this works for you.