As far as how you show your client-- well, that's really up to you. Some people will crop the final design and save it as a .JPEG, but I would imagine a .PDF is fine. I find that people in general understand images better, so I usually just send two images (one front, one back) to my customers for review.
As far as format for printing, your best bet is to contact your print shop and find out what works best for them. A simple phone call should be all you need to get their preferred file and size specifications.