For me, it was encountering my first Milotic, my favorite, forever and always.
I didn't look up any information of the pokemon before the game, everything was a complete surprise.
Then, I just had to have one!! And, my first Milotic hunt was so frustrating, exciting, among other things, but I was diligent. Then, by the waterfall I found a Feebas! I didn't know what they looked like. I was just so intrigued that such a perfect and beautiful pokemon would undergo such a transformation. But, I found out that I wasn't done. I had to collect them blue beauty berries, churn them with some old lady to make a pokeblock, feed them to my feebas, and max its beauty. By this time, I encountered my second most memorable feature of RSE, the competitions. I just remember how this new feature was just so amazing! (Unlike D/P competitions!)
Finally, I had one of these of my very own! Ahh, if only I could have some restrain with X and Y. :p