This question is actually more related with statistics or academia and in any case very general. For example you will need to worry about the statistical significance of the data and avoid hidden variables (e.g.: the Simpson's paradox). In the case of theoretical computer science this is probably not so relevant, as its nature is mostly qualitative. For applied or empirical computer science quantitative data may be of more interest.
The graphs that you should use are the ones that display best the data that you want to show. The data that you want to show will be different depending on the problem that you are solving and its characteristics, basically the dimensions of the problem and the solutions, focusing on the ones that are relevant (e.g.: principal component analysis).
Usually this is done when there are several approaches to compare and displaying the data as a graph helps to compare them, therefore the dimensions that are interesting are those that display the differences between systems in a way that is easy to understand, usually dimensions that are independent, but this is not necessarily the case always. Therefore, as there are previous approaches that already compare with the state of the art you can keep the approach found in the state of the art for the evaluation. For approaches that solve new problems there is usually nothing to compare with.
About the tools to do this and examples, I'd recommend TeXample. There you will find examples for graphs and diagrams that can be used on TeX. For related questions there is a sibling site: TeX@StackExchange.