When I used to go out to compete, I was also a spectator. Most competitors leave right after their matches, but I would stick around to get some ideas. The black belt kata competition would fascinate me, especially the advanced black belts (3rd and 4th dan). Some of the renditions of kata you'll see at this level can be very inspiring.
At some point we can figure out which kata we like to do. I had an instructor who would say, "there's white belt kata, there's black belt kata, and then there's your kata." But why do we like some forms and not others? Not that we should slack off on the kata that we think give us trouble (remember the Zen saying "the obstacle is the path"), but there's probably one you believe is best suited for you. This is true for a variety of reasons, including your level of athleticism and personality.
Here are my favorites
Seiuchin. This is a powerful karate form that comes from Goju-ryu. Features wide and deep shiko-dachi stance with plenty of angles and forceful breathing techniques. This ancient kata finishes with a corkscrew punch - peculiar to the Isshinryu system.
Kusanku. An aesthetic, challenging and beautiful karate form. I never had the nerve to compete with Kusanku. The truth is, you really need to be a certain body type to pull it off, at least for a tournament. I've seen a couple of entries butcher this one. If you have a large frame or lack a degree of flexibility, the jumping crescent kick halfway through this form may lack the finesse the judges are looking for.
Chatan Yara no sai. The sai is probably the only weapon found in Okinawan kobudo that didn't originally start off as a farming implement. The sai appears to have been developed to counter larger weapons, like the bo (long staff) and especially the sword. One reason I like the sai is because some of the techniques mimic what the hands would do in karate. If you really like the sai I would recommend getting a quality pair (like Shureido) as they are well balanced and can be handled easily.
It used to be held that every kata was the distilled essence of a fighting system. Maybe this is why the old-time masters would spend months and even years drilling their charges on a single form. Certainly they had their preferences: Choki Motobu is always depicted performing Naihanchi. Chojun Miyagi (and many others) felt that the kata Sanchin was of utmost importance.