Should I insulate my unfinished basement ceiling?
The insulation in the ceiling will have almost no effect on Uncle Bob's living experience, other than he may not hear as much noise from people upstairs.  

What you need to do is insulate the perimeter of the basement.  This would be all framing that meets with the outside of the house that is above ground level.  By just stuffing fiberglass or roxul into the joist gaps a good foot thick you will achieve 70-80% of your basement insulation needs for maybe $200 for a large basement.  

Also this needs to be done all the way around, not in just the area Bob lives.  I would certainly do his area first but even a small area not done can sabotage the effectiveness of the rest of the basement.  Also note that dirt is a pretty good insulator unless you are in an extremely cold climate so no use in doing the whole wall. 

And back to ceiling insulation.  In actuality if the basement does not have zoned heating and air, the insulation will probably make the area cooler in the winter.  The warm air from the first floor will not be able to infiltrate the lower level as well.  So if sound isn't an issue then I would not even think about going there.   (Most people would insulate the ceiling in a cold climate because they do not want the cold air from basement moving to first floor - not because they want to make basement warmer)