How to say "my" in Russian

When I first started to learn Russian, I was intrigued by the fact that there is more that one form of the word "my". At the time, I like the idea of a possessive determiner overtly agreeing with its nominal complement with respect to all phi-features (number, gender and case) captured my interest. It's an interesting linguistic phenomenon.

My opinion changed slightly when I realised that I have to learn all the different forms of "my". If you multiply out all of the different combinations of phi-features, one has twenty-four forms.

24.

Allow me to illustrate the source of my frustration:

мой моё моя мои
моего моё мою моих
моего моуго моей моих
моём моём моей моих
моему моему моей моим
моим моим моей моими

My more astute readers may notice that many of the above forms are identical. Granted. However, even when accounting for this fact, there are still thirteen distinct forms of the first person possessive determiner. Plus, I still have to be able to discern which forms are the same. Plus, there's some issue with animate accusative taking on the same form as the genitive case, whereas the inanimate accusative appears the same as the nominative. I believe. Honestly, I'm a bit hazy on the whole thing, and basically just say "мой" every time, regardless. After all, it really seems a drop in the bucket, since my Russian vocabulary is still limited to basic greetings, pointing and smiling, anyway.