After effects could be a good place to start, and I'd say with little experience, if you did go down that route, would be to look for templates. Search around for things like "infographics templates" or "motion charts" or "animated graph" charts templates or tutorials, just to point you in the right direction but those are just words off the top of my head.
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update: with a 2 minute google search i found this, albeit far simpler tutorial on animating graphs in powerpoint http://www.presentation-process.com/powerpoint-chart-animation.html#.VHIiIoepQVk and here's one that's a bit less colourful http://www.ellenfinkelstein.com/pptblog/create-the-effect-of-a-line-drawing-itself/ . basically google is probably your best friend at this point, with keywords like graph, animation, presentation, creator.