In my work, where the data is usually pretty simple, I tend to stick to some of the easiest charts to read:

I personally find that these work extremely well when it comes to comparing different elements.

Dr. Abela has created a system to help you know which type of chart you should use to present your data. He calls it the "Chart Chooser"

The team at the Financial Times has created a visual vocabulary that also helps you choose the right visualisation. This one gives you 9 categories (like Part-to-whole, Magnitude, Change over Time, Ranking, etc.). And for each category corresponding ways to visualise that.

Vitaly Friedman, the Founder/Editor-in-chief of Smashing Magazine, has written a good Linkedin post with many other links to such resources that help you choose the right type of visualisation.