How to choose between classification Vs regression approach?
I would say that the main thing is what information you think is the most valuable. There are some differences.

The benefit with a regressor is that it can give you a number of how much profit you can expect. That is obviously useful when considering a new product. The drawback is that it cannot tell you how likely you are to see this profit. It will not tell you if a product is risky.

Many classifiers can tell you with what probability it thinks a product will be profitable. This can alert you to potentially risky products. But the drawback is that you won't get to know how big the potential profit is.

As I said, it depends what you value most. But nothing is stopping you from training two models and using information from both of them to make your decisions.