It all depends on what you are good at. Here is a list of abilities which are relevant to sports and can be used to determine how good you are at something
Muscular endurance (stamina)
choose a sports which needs the ones from these you are good at. Or ifg you have preferences, by all means try them out and know for yourself if you fare well or you don't. trying the ones that interest you is the best way.
For fights, you can join karate, judo or other martial arts classes. I have limited idea about climbing. For Karate, you need to have good stamina and fast movements. Try to do exercises that help you perform better in those sports. For climbing, you need to have good upper body strength. So you need to lift weights.
You must remember that once you take a sport, you have to build up these abilities in you too. So think about what interests you more and then take them.
Personally, I love karate. though I am just an orange belt and had to leave midway due to an injury, I am recuperating with cardio and body strengthening exercises and will resume it soon.