There is no correct answer.
You have to learn them all and then be able to play them all. The normal progression is probably loose-passive (mainly because it would be a rank beginners 'no-nothing' tepid steps into the world of poker style), perhaps followed by tight passive (sort of depends at what stage a new players actually decides to start learning how to play) Then TAG, and finally LAG.
That is probably the path I took, and I'm not all that special. I didn't really begin to understand the game until I got to where I felt I understood the TAG game. That's when the natural transition to learning the LAG game occured for me.
All of this is conditional on just when a player picks up that first poker book, or finds Cardschat.
Keep in mind that the categories you provided are gross generalizations, and that personal styles will vary and migrate through the course of a tourney through that whole list.