copy address book to new computer

Greetings all. I have a Mac Pro 1,1 running OS X 10.6.8, and a Mac Pro 3,1 running 10.9.5. I am upgrading from an iphone 4 to a 6s Plus. I've have serious duplication of notes, contacts, and calendar issues for the last 5 years. My iphone 4 had hundreds of dups of contacts and notes that would not delete for anything. So I've gone through all notes and contacts and made all deletions, updates, etc in the older mac pro (which cannot go past the current OS X), and neither can load the latest version of itunes to connect iphone 6s plus. So I am in a bit of a bind to get the new phone set up. My thinking is set up the new phone on the newer computer as a new install therefore not risking any of the old corrupt info from older back ups on the old computer becoming an issue. But since I cannot (even if I wanted to) connect the new phone to the older computer's itunes for syncing, I would like to copy the entire address book, all notes , and calendars from the older mac pro, place the items in the correct locations on the 3,1 mac pro thus having immediate access to all of my calendars, contacts and notes to be able to sync/download them to the new phone with the fresh ios install. I do have some info in the contacts, notes and calendar locations for the newer mac pro, but don't mind deleting it all for the info from the older mac pro. So I am seeking the most convemient and accurate way to transfer said info from older mac pro to newer mac pro to have available for my new phone.

Sorry for the long winded question, but I am attempting to be as thorough as possible to ensure I get the best possible help specific to my question.

Thanks in advance.