Even though Deep Learning on Tabular data is a topic that is picking up interest, I'd try to stay away from it as much as possible. The main advantage of "statistical methods" (in contrast to Deep Learning) is the interpretability. Most business applications of Machine Learning happen on "tabular" data (explicit features) with a lot of knowledge by the company about the features selected.
A simple Decision Tree gives you AMAZING accuracy and you can still understand what's going on behind the model.
Interpretability in Business ML applications is, IMO at least, the single most important trait of the model selected.