When we first meet Brienne of Tarth in Game of Thrones S02E03, she's fighting in a tournament to impress Renly Baratheon, when she wins she requests the honour to serve him. There are several points where Brienne clearly shows she's devoted to him.
Why? From the viewer's perspective there are four kings at this point, why does she support Renly's claim and why does she show such devotion?