I watched Mahou Shoujo Madoka Magica during the summer of 2013. This was the first subbed anime that I watched. However, it wasn't my first encounter with anime culture, since I was already friends with many /a/ users on Google+. I had also read Katawa Shoujo when it was first released, so I read my first VN before watching my first anime—not something many people can say.
My favorite anime studio is Studio Trigger. I'm a big fan of all of their shows besides Kiznaiver and Darling in the FranXXX. I'm also a big Type-Moon fan.
I had a brief stint with fansubbing when I worked as an editor for Chihiro-Fansubs. However, I found it difficult to stay motivated since delays were rampant, so I quit. Believe me when I say that fansubbing is truly dead.
I've gone to a few anime conventions (Otakon, Katsucon, Anime Boston) but I don't really see the hype. I'm not super into cosplaying, most of the panels I go to are boring, and all I really end up doing is window shopping all the merchandise that I really shouldn't buy. The video game sections are usually pretty fun, but if I'm just going to anime conventions to play video games...
Here are some links: