Dave's right! I forgot to mention that, over time, it's possible that some of the shingles will come lose and fall down BEHIND the new siding. If this is the case, you'll get 'bulges'.
Thanks Dave for pointing that out. And one other thing. When choosing new siding, I recommend neutral colors like White, Bone, Baige, Tan, Grey, and so on. Should you decide to sell/move, it's easier to sell a house in this color than it is in, say, Brown or Cape Cod Blue or the like. When you get 'past' the asbestos thing, should you buy the house and want to vinyl it up, contact me directly and I can help with any questions. Try to ANTICIPATE questions. Keep your brain working more than 1 step ahead of yourself. This way, you minimize your problems.