What is the language / framework for a gamilization system?

Question

I will create a really simple game system (only credits, badges and levels at the beginning) for an existing website, but I really don't know where to start. Can you suggest me if there is an API or Framework or something else to start this development process. Website developed in PHP and jQuery.

I do not know how to start. I will really be attracting links, tutorials, books or something else to represent myself in the development of the game. Do I need a special database structure or special design patterns or architectural patterns?

Thanks in advance.