If you are going to make barberhartford your domain then yes, by all means 301 the old site, page by page to the new - in other words, do not simply redirect each page to the home page ... once that is done most of the link juice will pass to the barrberhartford domain, but the wise move is to have the old links changed, wherever possible, to the new domain.
The email address is not important SEOwise, and I don't know what NAP means, but I strongly believe it is very important for branding to use your domain name. However, I also feel that it's fine to use a name such as DixieCutters as the 'print' and promotional domain name; whatever people will best remember.