What is the recommended level of PHP for CiviCRM? There seems to be some inconsistencies
CiviCRM PHP requirements recommends PHP5.5 or greater, and notes PHP5.3.10 is the bare minimum required. As well as this, you want to be sure your PHP version is actively getting security updates, and also consider what PHP versions CiviCRM is tested with.
As of Feb 2016, I recommend PHP5.6 -

Support ended for PHP5.3 in 2014, and for 5.4 in 2015.
PHP 5.5 is getting only security fixes until mid 2016.
PHP 5.6 is actively supported until Dec 2017, with security fixes until Dec 2019.
CiviCRM doesn't run on PHP7 yet ... (CRM-17789: Support PHP7).

NB: Distributions may backport security fixes for older versions after those dates; please do your own diligence on whether your PHP version is secure :)