Predict Customer Next Purchase with Sequence
For sequence problems, I generally used Recurrent Neural Network. It has a property to learn its values, which is based upon the previous state and current input.
Since in your case sequence is important, you can use RNN. You can also try LSTM(type of RNN) cell.


  And Additional Note: For product suggestion(where sequence is not
  important) you can also use Apriori algorithm. This algorithm try to
  build association between the products of a single order.