It seems that you want to know which Slingbox model will work for you, if you want to watch a different signal while the TV set is in use at home. In this case, you will need to get either the Slingbox PRO or the Slingbox PRO HD. The main difference among these units is that the Slingbox PRO HD will allow you to get the High Definition signal.
These are the only models with a built-in tuner (it allows you to "split" the TV signal without affecting home viewers). You can also check this thread, in order to get further information.
The following links will allow you to get all the information about the Slingbox PRO and the Slingbox PRO HD.