POC - Get an idea to create a Predictive Model
Recommender systems are usually either collaborative ("other people who bought x also bought y") or content-based ("item y has similar properties as item x"). Given your very few data features, collaborative filtering seems appropriate. In the basic setting it could use only the purchases of your users. Ideally, you would also have some sort of rating of their purchases. 

Also, nothing stops you from using a hybrid approach with additional data if available.