Identifying Customers who are more likely to purchase a given product category- Which model to use?
Actually, I'd propose to tackle it from a different angle - assuming you want to predict product categories, and those are usually few, you can see it as a regular classification problem.

Every product group is a category, which you will try to predict. So you can use simple models, which are easy to train (logistic regression, decision trees etc.), easy to build, debug, explain and test. And you can experiment with various features - which ones are the most helpful when predicting product category (this is crucial, since many people will probably ask you why the model predict this category for this person).

Once you master this, then the regular approach to this is any type of recommender system (collaborative filtering, matrix factorization etc.). Plus you can use your simple approach as a benchmark.