Humidistats, in general, aren't very good, so expect a variation of 10 or more between humidistats. More so if the one inside the dehumidifier is ill-positioned relative to airflow.
Putting it near the furnace shouldn't be an issue, but if your ducts are leaky, or the unit emits lots of heat in heating season, it would reduce humidity around itself. It mostly boils down to air circulation.
Be sure you can use gravity, or a pump, to have the unit drain itself continuously rather than having a unit with a bucket you have to empty. The bucket thing is no fun at all.
Is there any water coming into the basement periodically or continuously? Humidity control is moot if the place gets actually damp or wet a lot, I guess for your aims you'd better look at humidifiers, you should definitely find something suitable from this article.