Claire is rich as seen when she only bought food from Falafel Phil's to feed her pug. She is fairly pretty and knows it because she was very confident that she would win the Pearl of Seaford beauty pageant.
She wants to win the Pearl of Seaford to prove to Kim that none of the girls at Seaford High can win the Pearl of Seaford. In Capture the Flag, she seems to have a crush on Jerry. She was seen again in Kickin' It On Our Own and has a crush on Milton.
Like most students that attend Swathmore, Claire is shallow and self-absorbed, judging people by their wealth. But she is also so shallow to the point that she flirted with Jerry for his looks alone.
Kim- Claire treats Kim like she were an ugly poor girl and goes far enough to say she isn't beauty pageant material. She thinks only girls from Swathmore Academy can win the pageant. When Kim came out of the dojo and bumped into her she called her a sweaty girl in pajamas. She also told Kim she shouldn't even bother showing up at the gymnastics tournament because she apparently had the better team.
Jerry- Claire has a crush on Jerry and tries to flirt with him even though she has a boyfriend (Monty) . This crush is mostly based off of looks because she is not aware of the fact he is clueless.
Milton- Claire has a crush on Milton when he attends Swathmore Academy and it is highly based off of his intelligence. She even goes far enough to watch him practice his French horn. However he turned her down when she asked him out, because he was dating Julie.