Can I purchase an iPhone from AT&T and still buy AppleCare+ from Apple?

Yes.

https://mysupport.apple.com/add-coverage/producttypes

Being an AT&T customer myself, I would never buy my iPhone from anyone other than Apple. Apple knows their products, and sets them up perfectly with an AT&T account.

Yes (but it may be a little easier to buy it through AT&T at the same time you buy your phone -- but if you want Apple Care be sure that is what you are buying rather than their insurance).

To buy it from Apple directly, see the following fromAppleCare Products - iPhone - Apple

How to buy

1. Purchase either AppleCare+ product with your new iPhone.
2. Or buy it within 60 days of your iPhone purchase:

• • On your device (go to Settings > General > About and choose AppleCare+ Coverage Available)
  • Online (requires you to verify your serial number and run a remote diagnostic)
  • At an Apple Store (inspection of iPhone and proof of purchase are required)
  • By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)