Which module should I use to visualize my Google Analytics Data using the Google Charts engine?
Seems to me that Google Analytics Reports is the solution for this, no? Those "reports" do include charts also (not just tabular data).

If you rather want to create some charts yourself, consider the Comparison of Charting Modules as a possible place to do start from, to find the module that best fits your needs. Possible alternatives that might work for this specific question are the Chart module, or the Charts module, though there are other alternatives in that comparison that might be a better fit for this case.

The license that comes with the related charting library (engine) in each of these modules, should be considered also. It is one of the (important?) selection criteria for deciding on the module to go for. 'Possible privacy concerns' or 'Yes or no support for saving charts in PDFs' is another typical item to consider.

Disclosure: I'm the author of the comparison and modules Chart and Charts, I hope this does not violate the site's policy on self-promotion.