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Finishing off part of a basement. It's 13x17, which yields an estimate
of 5270 BTU's to raise the temp 15 degrees. I have gas/hot water in
the rest of the house, but it seems overly expensive to put the
plumbing in for that, so I was thinking of electric baseboard.


That ia bout 1500 watts. You can figure the operating cost easy enough. It
will be more expensive that using the existing, but you already know the
facts there.


Also, I see differing opinions on the desirability/need for foam
insulation between the walls and studs. Some books simply recomend
moisture proofing the walls with appropriate paint, others say you need
to put foam insulation between the walls and studs to prevent moisture
from condensing/rotting/mildewing the wood. Does anybody have any
insight into the differences in opinions?


Forget the paint, mildew, etc. Think about the cost. It is just plain
irresponsible not to insulate the basement walls. You will save energy for
many years to come. Oil was $58 a barrel today. That should answer the
question.