How familiar are you with Mathematica and the Wolfram Language? If you're new to Wolfram Language, then I recommend you don't pursue any OO programming until you've learned the evaluation paradigm that Wolfram Language uses. If you don't have a good grasp of how WL works "naturally", then trying to do OO in WL will just wrap you around the axle.
If you think you're proficient in WL, then the next question is "what do you actually want to implement?" It looks like you are focused on inheritance, but that's not necessarily the most important part of OO--many people wouldn't even require inheritance in order to call something OO.
Anyway, you might start with
