Sure, you can definitely apply a classification method followed by regression analysis. This is actually a common pattern during exploratory data analysis.
For your use case, based on the basic info you are sharing, I would intuitively go for 1) logistic regression and 2) multiple linear regression.
Logistic regression is actually a classification tool, even though the name suggests otherwise. In a binary logistic regression model, the dependent variable has two levels (categorical), which is what you need to predict if your customers will pay vs. will not pay (binary decision)
The multiple linear regression, applied to the same independent variables from your available dataset, will then provide you with a linear model to predict how much your customers will pay (ie. the output of the inference will be a continuous variable - the actual expected dollar value).
That would be the approach I would recommend to implement, since you are new to this field. Now, there are obviously many different other ways to define these models, based on available data, nature of the data, customer requirements and so on, but the logistic + multiple regression approach should be a sure bet to get you going.