I can't understand from Apple's docs if I need a production certificate or a development certificate...
You need to create a Distribution Certificate. The Distribution Certificate are used for creating Distribution Provisioning Profiles. Which will allow you to do the following:
Below are the Apple steps on how to create an Ad-Hoc version of an app
Ad Hoc distribution allows you to share your application with up to 100 iPhone or iPod touch users, and to distribute your application through email or by posting it to a web site or server. To prepare your application, the following steps will need to be completed.
Hope this information points you in the right direction. If you need additional details or walkthroughs just let me know.