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.
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.
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.
Indoor structures made of concrete or plywood are erected, into which artificial footholds and handholds are fixed. As it is indoors, the height of the ceiling limits how high the structures can be. There can 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.