Title sequence

First title that comes up is on 00:06 and mentions Peter Dinklage. It is a very famous character in the series and also a very popular and liked actor so it catches your attention and suggest that this is going to be a good series because of good characters. Martin felt there was never anyone for Tyrion but Peter Dinklage. No one else read or was auditioned, they "just had to get Dinklage" and he was "incredible from the start. 

The next actress mentioned at 00:08 is Lena Headey. She is a outstanding supporting actress in the drama series for portraying Cersei. As her carrier starter when she was 17, she's well popular actress with great acting skills such as Dinklage.

As 3rd mentioned character at 00:08 is Nikolaj Coster-Waldau. He is well known from the fact that he played in lots of films and tv shows since 1994.
The first 3 displayed characters are higly known so they are mentioned first because it makes it look more interesting, while on other hands film producers usually put main character first.