How to change default contact template
This isn't a feature in iOS 8 or iOS 9.

If you don't want a new number to be categorized as "home" you need to tap and change it. Luckily, third party apps can and do provide more customized interfaces to your contact database.

I would start with a tool like Interact for setting up a more flexible default contact addition interface as well as extending concepts such as groups and smart parsing of contact details.

The time you save with one-tap contact addition and share sheet access to this app will more than make up for the expense and effort needed to have a better tool for contact management than ships with the OS.