Hi Judi
Adding a very little amount of rennet will mean that you need to rely primarily on getting a lactic acid curd (commonly used when making higher water content cheeses), adding a lot means you are making a rennet coagulated curd (commonly used when making lower water content cheeses). It depends what you are trying to make, see
Wiki: Coagulation for more info on coagulation methods.
Ripening overnight without adding a starter culture I think would only be good for raw milk where you are encouraging the native flora to build and acidify the milk, in which case you could go without a starter culture. Doing this with pasteurized milk could result in unwanted microorganism growth.
On which method is best, depends on what you are trying to achieve, there's
a thread here with some info on Chaource where I wrote that one book I had said it is an AOC cheese and is supposed to be made using lactic acid coagulation.
While above is not a great help it's a start.