I'd be ok with calling any of the following three purchases my favorite:
Persona 3: I bought because I thought it was cool that there existed an RPG with life sim elements. It turned out to be much more than that though, and to this day remains my undisputed favorite game of all time.
Deus Ex: Got this for about $5 in 2008, not really knowing what it was. I was expecting a run-of-the-mill FPS, but holy shit did my mind get blown when I realized just how expansive a game it truly is.
The Legend of Heroes Trails in the Sky: I'm not even sure why I wanted this game so much. Like Deus Ex, it looked like a rather generic game at first. But it turned out to be so much more than that.