I've been climbing for 3 years now and I intend to climb for the rest of my life. I love the sport! I live in London so mainly do indoor stuff at rope walls or bouldering walls. Whenever possible I try to get outdoors on real rock as that's what it is all about!
Climbing is definitely addictive but it might not be for everyone, particularly if you don't like heights too much. It's worth trying both disciplines before you decide if you like it or not.
There is bouldering where you don't need anything but rock shoes and some chalk. You climb relatively low height walls (maybe 5m max above thick crash mats) and the "problems" you climb are solved by a particular sequence of moves that are usually more powerful or technical in nature compared to those you find on a longer rope climb.
Rope climbing is the other discipline where you require a rope, harness and a climbing partner to belay you. You can rent all the equipment at the wall until you decide you want to buy your own. The routes you climb with a rope indoors are typically over 10m and can be above 15m depending on the size of the climbing centre. You can either "lead climb" where you clip the rope into carabiners yourself as you climb or "top rope" where you are always hanging from the rope so can't properly fall (unless your climbing partner drops you!). Top roping is usually the place to start until you get experienced enough to try leading. Rope climbing, until you get to the higher difficulty levels, is more endurance focused compared to bouldering. I like to do both to try and be a balanced climber, but personally I prefer bouldering.
Besides the physical benefits of climbing, I'd say it is a really great sport for socialising. Compared to the gym where everyone listens to music and ignores everyone else, at the bouldering wall you can chat with others about how to do a problem and compliment females on their "form" without sounding creepy.
Obligatory photo of me: