What are the main topics to master in order to learn to play the piano?

If one wishes to take private lessons or perhaps some other means of formally learning the piano, what are the topics that one must cover and in what order? Which topics are usually the hardest and thus need the greatest amount of concentration and practice and by one point along this line is a person at "intermediate" level?

My intention here is to understand a typical flow that a person goes through when learning piano when we wish to learn something we start from a certain topic and build on that and learn more new topics later on and than combine all of them as we progress. I myself am from an electronic engineering background but wish to learn piano so I can play my favorite songs and also be capable of sight reading other game piano compositions e.g memory of light and waves, The Sims build mode songs among others.

I am posting this question as myself and many others that wish to learn this instrument and have no prior experience of any musical instruments would like to know this.