If you have had water problems only on the side that is unfinished and will remain unfinished, I would go with the addition of the sump pump to that side.
The sump pump can only help in reducing the water level under your floor and minimize the possibility of future water on the finished side.
One thought on the carpeting for the finished side.. You might want to consider the use of the type that has the padding attached, and just cut it to fit. That way, if the carpet ever does get wet, you can roll it up and carry it outside to dry. Just a thought..