When I got my 6s I didn't buy the extended Apple Care warranty, can I go back and purchase it?
For iPhones you have 60 days from the later of date of purchase of the device or date of delivery/activation of the device. You can do it online, at an Apple store or by phone (1-800-MyApple). They will run a remote diagnostic if not purchased in the store or run the diagnostic and do a visual inspection if purchased in the store.
Waiting to buy has no effect on the term of the AppleCare+ coverage - it's two years from the later of date of purchase of the device or date of delivery/activation of the device. So, waiting 60 days to purchase it will not get you an extra 2 months of coverage.