Predict customer action from previous buying history
You can have a variety of solutions, starting from very simple to a more complex and beneficial ones.

I suggest that you'll start with the simple solutions, jain much of the benefit and continue by need.

Note that though the problem can be treated as a supervised learning problem, it is a multi label problem (a customer can be interested in many services). Therefore, decision tree or logistic regression is not suitable (unless you have a handful of services and you try to predict if the user would like a service, for each service).

The classical method to provide such recommendations are "People that like X, also liked Y". Though very simple, at time 50% of Amazon's revenues where due to that.

You should make the recommandation more sepcific by considering the lift - Harri Potter is very popular and many people like it. However, it isn't the most sutabile recommandation for someone reading browsing books.

You can take such a item-to-item recommendation and use all user history by aggregating using Naive Bayes or similar methods.
You can take care of temporality and dates by giving more eight to recent data.

The next step is moving to recommendation system. You can find on the web some implementation. 
The winner in the Netflix challenge used matrix factorization algorithm, so this direction is very popular for recommendation systems.