The best way is to just experiment, I think. Remember that Lightroom doesn't do anything to the original files. So you can experiment on you want and you won't hurt your images. I would probably try the auto adjustment first and then go from there. Others may have better ideas, but that is what I have done with a lot of old documents and it has worked well for me.
Yes, all the enhancement tools in Lightroom can work with document scans (or photos).
Lightroom requires you to "Export" an image with edits which is the equivalent of 'Saving a copy'.
Extensive repair work (like lots of spotting) would be best done in Photoshop (or another pixel editor)
My screen-clip shows before and after of a book cover scan. The only work done was with the "Spot Removal" tool in Lightroom (took 5 minutes!)-
Thank you and to Jim Hess also for your replies. The documents I am dealing with are mainly b&w and what I would be trying to do is sharpen handwritten text, correct contrast and other things which resulted from documents which were scanned and whose print settings were not tweaked when print outs were made. I know from looking at scanned images online that adjusting settings online before prints are made or the document is saved as a new jpg can make a huge difference, and it is probably not ideal to take prints which were not so corrected and then try and correct them from the hard copies which were provided to me and then rescanned as jps. The image I scanned from the hard copy which was sent to me is going to be hard to imrpove upon, I would think, so I probably should try to get my hands on the originally scanned jpgs and generate better images from them, if I can do that. Alternatively, I assume that Photoshop may be able to tweak the images but I'm not sure, or I could also try Jim's suggestion and just experiment in LR.