Most Full Sized DSLRs Should Do the Trick
There are a large number of choices for DSLR camers out there. I would recommend a Canon or Nikon if you can afford it. But you really don't need to go all out for the big bells and whistles. Instead you should look at one of the entry level DSLRs.
This part is IMPORTANT!!! If your archives are important to you and you want to get the best images possible, you should probably consider spending less on the DSLR (maybe even a used one) to allow for the cost of a really good lens designed to do copy work. Remember that your work isn't going to be flat, and as such, it will be difficult to get razor sharp images across the entire plane of the copy. It would pay to do some research on this selection.
As far as scanning goes, it provides a possible solution. Most scanners these days have a capability to open the top to enable scanning anything you can lay flat on the glass copy surface. If you're going to have to handle the books anyway, a scanner with a removable lid may do the job. Scanned images are very sharp and capture every bit of detail you'll get with a camera. I wouldn't rule this out as an option.