A few pointers for starting rock climbing / indoors climbing:
1) Dont bother trying to get fit before getting started with climbing. You will have more fun getting fit while climbing anyway. Unless you know very well what you are doing, gym training does not easily translate into climbing fit anyway (later on it will help you out more)
2) Size matters, but don't focus too much on it. I started climbing again after years of doing nothing but office work, and I was pretty big: 246 pounds to be exact. Was climbing hard? Yes. Would it stop me from climbing? No.
Most of the instructional stuff out there on the Net about getting started with sports climbing (I use the term loosely here) is not really for beginners. I think the stupidest thing the climbing industry has done is to make sports climbing into something mystical and almost magical. They try to tell you that you should read at least 4 different books, spend 6 weeks preparing yourself at the gym working out according this or that training program, attend a course with a personal instructor. And I say they just want your money.
When I get asked by people how to get started, I usually tell them to take their normal gym clothes and go to the nearest indoors bouldering gym. They usually rent you gear as well, and 12 £ or so should be enough to get you shoes, a chalk bag, and entrance. Since it is a bouldering gym, you dont have to worry about safety gear etc. You wont get more than few feet off the ground, and if you fall you will land of soft cushions. And if you were able to climb trees when you were 6, you will be able to do it again.
Once you are comfortable at a bouldering gym, you may wanna start top-roping and by this time a course is a good idea, even for just safety purposes.
Bottom line: dont make it too complicated.
(Oh, and one more thing: Dont worry about getting too much muscle or becoming Madonna. It just doesnt happen by accident.)