Go and 'fish' your way through the bowels of these Posts/Follow-ups and read what I've already written about Asbestos Cement Shingles. Asbestos Follow-ups
In short, I'd have the shingles removed no matter what new siding you choose (if you choose one.) They can be easily painted if you 1) clean them with a low-power pressure washer, and 2) prime them (where the paint has come off), and 3) paint them with a HIGH QUALITY paint from a Paint Store (found in the YELLOW PAGES under PAINT - RETAIL. Just tell them what you're painting ...)
I've written info about the potential hazard in the aforementioned follow-ups. If you have any 'difficulties' w/all this, e-mail me directly. My best to ya and hope this helps.