Which PHP/MySQL version should I use? We plan on updating our Drupal 6 (with MySQL 5.5x and PHP 5.x) site to Drupal 7.

Which version of PHP and MySQL should I choose?
You will get the best speed performance using PHP 7.x. I've been running a few Drupal sites on PHP 7 with no issues, and definite performance improvements over PHP 5.x.

MySQL 5.5 or 5.6 is good.