You will want to climb first, level to build speed, then go head-to-head, so the climb speed doesn't really matter too much in this case.
However, just to name a few of the best climbers in the game, there's the spit8/16/14, the 109 g2/k4, the c205 matches the 109g2 for climb, the ki84 isn't bad, the f4u4, and if you want to try something wacky, let's not forget the Me163.