What is the best way to choose a natural looking tooth shade?

This depends on wether you want something age appropriate or maybe going a bit whiter, you can start with a natural white shade and compare shade tabs to where you are on your natural teeth or existing denture. 

Hi and thank you for your question. 
There are many ways to pick the best shade for your all on four teeth. You can match the shade with your own teeth with a shade guide or there are devices that determine the actual color of your natural. In all picking an extremely white shade will make your prosthesis look fake, because no one has extra white teeth, but at the end the best shade is the one that you feel most comfortable with and the one that matches your personality.
Good luck and I hope you get the smile you are looking for!!
Dr. Juan C. Arroyo
Oral & Maxillofacial Surgeon

Are you getting two sets or one set of all on four (first set is a temporary set placed following surgery)? If you are getting two sets of all on four  I would start with A1 shade as it is fairly natural white, and then by the time the final set is fabricated you could decide if you want to go whiter or not. Talk to your dentist, or perhaps stop by the lab to see some samples of A1, B1, or even bleach shade teeth on the all on four.