A visualization is meant to communicate something about patterns or comparisons in the data. Choose a chart, graph, or image because it effectively communicates a data narrative. Do you need to show change? Display distribution? Something else? Let the purpose guide the visualization. You'll also have to consider how many variables you need to display, as some types of charts and graphs are limited in how many variables they can show.

Remember, in your visualization, you must balance between form and function. It is possible to create a visually pleasing but incomprehensible visualization or a boring but easy to read one. The most effective graph will be clear and attractive.

Check out Chartio's tutorial on choosing visualization types.

Infogram includes best design practices for each type of visualization.