Identify the ideas you wish to convey. If you want to illustrate a change over time, a line graph is probably best. Pie charts are best at comparing differences of parts of a predetermined whole. Use bar graphs to compare things in different groups.
Look at the quantity of data to include in the chart. A double-line graph can show change over time as well as compare two groups. A bar graph can compare a two groups or several groups. If you want to show information for several groups, a graph that shows data at a specific point in time will be easier for an audience to read.
Define your audience. Pie charts and bar graphs can be very easy to read and illustrate the intended data. They are often appropriate for younger or less technically savvy audiences. Double- or triple-line graphs might get confusing because of the large amounts of data being represented. A scatter plot, which uses single points to illustrate relationships between two different things, might be better for audiences that are familiar with the graphed information.
Decide how you will present the graph. A large, easy-to-read graph with few specific details might be more suitable to present in a slide show to a large group. A more complex graph with very specific information might be better for a handout.