How to go about developing app using PHP being employed in wordpress?

I wanna develop - something like vocabulary builder - where words and related attributes are stored along with difficulty levels - as per standard (students for example) and then build few innovative games around it - where students may further be rewarded with some reward points similar to one used here in these forums.

Do I need to develop plugin for this? or there is some other way out also? (Probably which one is simpler)