Can I sync my new iPhone 6s with my iPad?

You can sync that iPhone with the Mac - if you want to sync it with the iPad just sign in with the same account on both and use Continuity to enable the sharing of messages

Also enable iCloud Photo Library on both devices to share images

Use Continuity to connect your iPhone, iPad, iPod touch, and Mac - Apple Support

As long as both devices use the same Apple ID they can be synced via iTunes or iCloud.

Your wife should have her own Apple ID and user account on the Mac, to keep her and your information separate. If you want to share purchases, such as music and apps, you can set up Family Sharing.

I think my question is similar enough that it can be in the same thread...

How do I sync my iPhone 5 to my iPad without access to the internet? Usually I back up my iPhone data and images to a MacBook Air, using USB.

For an upcoming project, I have an iPad2 available, but no internet or cellular.

Any and all sync of this type requires a network connection. You cannot transfer data between 2 iOS devices with USB, but you could (sort of) fudge it by using a Mac with iTunes as an intermediary - but iCloud over the internet is a far, far better solution.

I was just looking for this too, thank you very much @Rysz