Chef will take you much longer to learn and though it has some really nice advanced features, it's overkill if you don't need them. Ansible is fairly straight forward to get started and get what you need done. The only problem is it doesn't work with Windows if you host any Windows boxes whereas Puppet/Chef have Windows support. I personally would first go with Ansible then try Puppet if it's not enough.

To add to the mix. I'm doing both. Ansible for the provisioning and coordination/install/running of chef. And then chef for the recipes because there was already an investment there at the time.