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You will have to break down your application as it is a humongous task to create something like GA.
You will have to track many user activities(click,spend time etc).so you can do that in plain js or use a cross-platform lightweight library(angular.js) that can make your life a little easy.
Now since you will have to send large set of traced data to you database with minimum latency,use Node.js in this scenario.Simple Ajax call would also work but then it would be very slow.
Now comes your database.Prefer NoSql since it suits your requirement of unstructured data ,preferrablly MongoDb which can help you with its own mapReduce,large storage capacity
.Since there will be lot of calculation involved you can use your python knowledge which can help you process data a lot faster.you can use other languages as well(eg.Go)
Your processed data and results can then be stored in Redis(which acts as a caching layer).
you can use sophisticated graphic library like d3.js,Highcharts.js for displaying Graphical data on the client-side.
There are a lot of factors that can be involved.This is just a very basic outline of what you could do.