I have a problem deciding what to use since i'm just beginning to creating predictive models.

Let's say I have a training dataset with 5 or 6 features and a testing dataset. (With around 50k rows in training / 5k in testing). My samples are people that I would like to assign to types of products they would buy. (more than 2 classes).

I'd like to know the whole process of what to use, and based on what exactly. Also, is there a serious difference between the results rendered by an ANN and other classifiers on this type of classification?

Note: I have 10 possible classes in the output

Thanks in advance.