If you can take classes or visit a rock climbing gym and practice with ropes first that is definitely a plus. Climbing with ropes up a wall as simple as the ones they offer at local amusement parks will give you an idea of your own upper body and lower body strength. Though your best bet is to try a rope climb with a minimum of 50 feet to start. That will do a small job of testing your muscular endurance as well.
Climbing is actually mostly about finding the proper footholds and using your legs to push yourself up, but there are times when your footholds may break off and just in case you ALWAYS want to be strong enough for one of your arms to be able to support your entire body weight. It's also important to make sure your upper body is strong enough because a major thing that beginners do is they try to find handgrips and they attempt to pull themselves up. The biggest mistake is when someone is reaching out with their fingertips to grab the next hold and then they jump a little, grab it, and wind up needing to do a chin up because their feet are no longer on those lovely little footholds they had before. It's best to go for handholds within your easy reach so look for the easiest ways up to start.
To answer your question I actually never saw an artificial rock climbing wall until I was 17. I grew up in a rock climbing family so just always went with them, and they taught me how to. In high school I taught some of my friends how to do it and we would do small climbs without ropes. (By small I mean about 15 feet, I do NOT recommend that anyone try that unless they are over deep water because 15 feet is acutally a story and a half.)
I would also steer away from any mountains for a few years. It takes time to really perfect it and get quick enough to react if something happens. I've been doing this since I was 12 and am probably the only person I know who rock climbs who has not broken anything, and that has been just through dumb luck on my part because I have had some nasty falls. My worst was probably 25-30 feet into water. Not fun, very painful, and it was a nice reminder to my ego. ALWAYS climb with ropes and make sure to talk to someone at a store who actually knows what they are talking about. Do not take advice from someone who was just hired at Dicks Sporting Goods and has no clue about how to use the equipment.
So if you use ropes as often as possible and are smart about it you'll have a great time! Hit me up with any more questions that you have!