Terry, I don't understand the renaming. Did you do a typo somewhere or am I just misunderstanding your intent?
Batman, the word "select" is causing you difficulty. You need to do a "selection" operation twice.
First:
View/Switch to Product (or use the map selector dropdown list).
Second:
Once the desired map (in this case your World Basemap) is being displayed on the screen you need to select which parts of it you want to transfer to Mobile PC.
Mapsource is designed with the idea that you will be using a handheld GPS device with limited memory. Most of Garmin's map products come installed in segments. That is, there are actually many many files required to make the entire map that you see displayed in Mapsource.
So Mapsource expects you to select the map segments that you want to transfer to your GPS device. The error message you got means that you have selected a map for Mapsource to display but you have not selected any of its map segments to transfer to the GPS device.
I don't know if the World Basemap has many segments or if it is just a single large segment. In any case, after you have selected the World Basemap to be the one displayed in Mapsource, you must then use the selection tool (TOOLS > MAP) to select some or all of the World Basemap.
If you have selected the correct tool, the cursor will have a broken rectangle beside it as you move it around the map display. You must click it on a map segment and make it turn pink to select it. When you do this, the name of that map segment will also show up on the list on the MAPS tab at the left of the screen.
You must have one or more items listed in the MAPS tab or Mapsource will continue to give you the same error.
I hope that helps. All of the information you have provided makes it clear that you will have success transferring the World Basemap to Mobile PC as soon as you select some or all of its segments to transfer.
...ken...