Next basket recommendation is a critical task in market basket data analysis. It is particularly important in grocery shopping, where grocery lists are an essential part of shopping habits of many customers. In this work, we first present a new grocery Recommender System available on the MyGroceryTour platform. Our online system uses different traditional machine learning (ML) and deep learning (DL) algorithms, and provides recommendations to users in a real-time manner. It aims to help Canadian customers create their personalized intelligent weekly grocery lists based on their individual purchase histories, weekly specials offered in local stores, and product cost and availability information. We perform clustering analysis to partition given customer profiles into four non-overlapping clusters according to their grocery shopping habits. Then, we conduct computational experiments to compare several traditional ML algorithms and our new DL algorithm based on the use of a gated recurrent unit (GRU)-based recurrent neural network (RNN) architecture. Our DL algorithm can be viewed as an extension of DREAM (Dynamic REcurrent bAsket Model) adapted to multi-class (i.e. multi-store) classification, since a given user can purchase recommended products in different grocery stores in which these products are available. Among traditional ML algorithms, the highest average F-score of 0.516 for the considered data set of 831 customers was obtained using Random Forest, whereas our proposed DL algorithm yielded the average F-score of 0.559 for this data set. The main advantage of the presented Recommender System is that our intelligent recommendation is personalized, since a separate traditional ML or DL model is built for each customer considered. Such a personalized approach allows us to outperform the prediction results provided by general state-of-the-art DL models.