1) Is it something to be unduly concerned about? Joe's right in all respects. 2) Will it affect resale value? Joe's right in all respects. I had it on my home. Out of 17 homes in our little development, 14 still have it. So, to have it in my neighborhood is just fine because it's "still in character" with the rest of the neighborhoor. If you were to update your siding, certainly, you'd increase the value of your home. (How much, depends.) At the same time, you'll actually 'bring up' the value of the OTHER homes too. It's just a side-effect. That's OK because after I did mine, in the last 2 years, 2 other homes have joined me. (Hence, 3 out of 17 have vinyl.) Now, if it were that 3 out of 17 homes had VINYL siding, the remaining 3 that had asbestos siding may actually 'bring down' the value of the 14 that have vinyl. So, you see, as Joe says, it depends. In short, 'updating' your home is fine as long as it's not out-of-character with the other homes in the neighborhood, and you stay long enough to recoup the expense. Generally speaking, in today's market, it will take 5-9 years to recover the expense depending on where you live. NOW, as on another aside, if you were to reside with, say, cedar shingles, you'd be out of character because unless the other homes have it or plan to have it, you might be the only one with cedar siding. Sooo, you need to think about what you want to use for updated siding. (If you have specifics questions on this, e-mail me directly.) 3) Are certified, asbestos contractors very expensive? Joe's right in all respects. The good news is that there's a good chance you won't need one. BUT, to be sure, check with your local municipality on their 'laws' regarding non-friable asbestos. In my jurisdiction, the owner of a single-family home is permitted to remove the siding w/o any permits or men-in-white-suits. I will say that these laws are evolving. As more and more states, even the feds, look at non-environmentally friendly materials, this is one that's being talked about! So, I say, if you can afford the 'change' and you plan on staying a while, and you'll reside in characater, (and so on), do it. A home inspector, as you know, will be telling prospective buyers that 'the home has asbestos'. Now that you know it's, basically, harmless in its solid state, what are the chances the a prospective homeowner knows that? Many states already require Seller Disclosure. Demand one if you're buying. Talk to your agent about what it is.
Now, to say more beyond your questions ... For all intensive purposes, you can put up new siding over top of the asbestos siding. However, I don't recommend it! 1) Depending on what's underneath the existing siding, it may not hold. 2) a 1/2" (minimal) flat-surface 'board/material' will need to be nailed over top of the existing siding to create a flat surface. This is because the new siding's warranty may be voided if it ISN'T done. 3) It's been known for the existing siding to 'fall off' the covered wall! If it happens enough, or just right, you'll get 'bulges' in your new siding. 4) Seller Disclosure is becomming more and more common place. If you're required to fill it out when you go to sell, you'll have to say that you know what's under there. If you don't and the 'new' homeowner can prove you knew (like finding out who installed the new siding and when), you MAY set yourself up for a lawsuit.
You can do the demolition yourself if you're up to it. If you need more info on this, I'll spare you now and you can e-mail me directly. My best to ya and hope this helps.