Firstly, Italics are supposed to be used for highlighting or for specific reasons. NOT to post an entire question.
Top Gun selection is done at the end of your JO sea duty tour in your F/A-18 or F-35 squadron. You apply through your weapons school. The selections take place quarterly to happen just prior to the quarterly detailing of JOs to shore duty. When you apply, you express your desire as to whether you want to go to the weapons school or stay on at Fallon as an IP (and I think there are a couple of other rare opportunities like Strike, RAG, VX). It is recommended that you 'rush' wherever you want to end up a bit before you put in your package as they will have a lot of say as to whether or not they want you.
What do you have to do to be selected? Meet the minimum requirements (which almost everybody coming out of their fleet tour does) and be wanted in the patch-wearing community. That's about all it comes down to. Helps if you are good in the jet and not a total douche (though some would argue about the douche part.) In my experience, mostly good dudes get selected. It seems like a good way to go if you want to be a Tactics Instructor. It is NOTHING like the movie, and the school is just basically a school to get you a qual to be an instructor in a shore tour. If you don't want to do any of the jobs that patch-guys do, then there is little good to come from going to Top Gun. Until you've been in the fleet about a year or two, you should not even be thinking about whether it is something you want to do because in reality, YOU HAVE NO IDEA!