You do not need to be athletic to take up the sport of rock climbing. Of course you need some sort of stamina, sense of balance, and strength, to do well at this sport. Nevertheless, depending on your preferences, you could choose from the various types. Here they are...
Conventional Rock Climbing
This is the kind that is usually shown in movies, with pairs of climbers connected with a rope, ensconced in harnesses, scaling up vertical rock faces, carrying specialized equipment in racks. As they climb up, the climbers fix nuts, wedges, and other types of protective gear into the crevices in the rocks. The rope is tied to these, so that in case a climber should lose his/her footing or grip, the rope prevents the fall.
Sport Rock Climbing
This type is similar to conventional rock climbing, the only exception being that the protective gear is fixed to the rock permanently. Hence, climbers do not have to lug all that gear up and fix it along the way, which makes climbing faster, less expensive, and safer.
In this, as the name suggests, instead of climbing up crags and cliffs, you climb up boulders, which are usually about ten feet or so in height. Since the climb is not very high, boulder climbing is usually done without ropes.
In this type, glaciers and frozen waterfalls are scaled. Instead of using nuts, cams, and wedges, specialized equipment that can be screwed into the ice is used.
Free Solo Climbing
This is just like normal rock climbing, except that no protective rope is used. Hence, if the climber should fall, it usually leads to death or grievous injuries.
Indoor Rock Climbing
Indoor structures made of concrete or plywood are erected, into which artificial footholds and handholds are fixed. Since this is indoors, the height of the ceiling limits how high the structures can be. However, the advantage is that there are never any inclement weather conditions to deal with, plus, the footholds and handholds can be unbolted in order to reconfigure the climbing surface.
As you can see, each type differs either in location or equipment required. Choose the one that you feel you would be comfortable doing, before moving on to the more difficult ones later on.