I always look for as little drop (difference in heel thickness and forefoot thickness, in mm) as possible so feeling the floor is better and you have your natural balance in play without unneeded cushioning. My trainer does fitness and powerlifting competitions and says that Converse is the only non-sport specific shoe they allow in competitions. Maybe start there and see about whether or not you want to  think investing? I have New Balance Vazees but they're a 4mm drop, I only use them because they were free vs. $40 for converse at an outlet store.