Wow, welcome to the boards and congratulations on deciding to take on this great adventure! I really admire rockclimbers! Just the other day, I was walking a trail w/ a friend and saw a group of climbers, they were in such great physical shape, and talk about strength and agility. You really need to know your body and be a total comfort and confidence w/ it to rock climb, don't you think?
Well, you're starting from a clean slate, that's great. Regarding budget, the fact that you can rough it out and camp is a great thing! When do you think you might go, spring/summer is more expensive and crowded, so you'll need to plan some things in advance, including researching cheap flight deals and even reserving camp sites. Go to the internet and try to find the best rockclimbing locations/cities. Then you can plan your traveling route/itinerary around that. How does that sound?
In Europe, like everywhere else, touristy locations are a drag due to the crowd and commercialization, but don't totally cancel them out, for their have their own magic if you can look beyond the touristiness and it can be a good starting point (information wise and meeting people wise) before you head to the more remote locations.
What other interests and/or specific questions do you have?