In reply to DoorRaider:
Hi Andrew,
Climbing inside and outside are activities that manage to be very similar and very different at the same time. Most people nowadays get into it at a climbing wall, though that's by no means essential - it's useful though, as most climbing walls do "beginners' courses" where you can learn how to tie in, belay safely etc. while climbing on plastic. If you have a friend who climbs, they can teach you the same.
Climbing outside is more fun
Again, you can either pay for instruction or get a friend to show you. There are a lot of SPA/MIAs in the country who run climbing courses (SPA=instructor who can set up ropes on single pitch, short crags; MIA=mountaineering instructor who can take you climbing virtually anywhere), and Plas y Brenin is the national mountain training centre. There might be local people on UK Climbing who can take you climbing outside if you post on the "Lifts and Partners" section - make sure you can belay safely before you do this, though!
One disadvantage of booking a course at the moment is that the weather is going to get more unpredictable, and a weekend in the rain is unlikely to kindle that passion as much as a crisp, sunny day with birds flying below you
Don't buy kit until you've had a go. A good instructor/beginner's course will be able to give you advice on what you need, and you'll be able make an informed decision. For inside climbing, you can hire everything from the wall (initially) anyway. (Eventually you'll want shoes, harness and a belay device and karabiner, though.)
Finally, climbing is a sport where the safety comes from what people do (i.e. with no safety system in place, it would be incredibly dangerous - but an effectively used safety system removes a huge amount of risk). As you learn, learn to judge whether the friend/Youtube video/post on UKC seems logical and can be trusted, or whether the person is BSing. That will keep you safe.