My interest in anime started in April 2013 when I got quite into Studio Ghibli films, my favourites to date being Porco Rosso and My Neighbour Totoro. However, the first anime series I properly watched was Attack on Titan season 1, which was in preparation for MCM London Comic-Con in October 2013. Some of the staff from the show would be doing a panel there so I figured I'd at least check it out. As it turned out, I loved it after watching all 25 episodes, and even though I didn't get to see the panel at the con, it was great to see all the cosplayers that were about! (I'm not as crazy about it nowadays but may finish watching it someday)
After this I decided to try out the anime society at my university, which, on top of being a generally awesome place to meet new people, introduced me to several more anime series that were new to me. I ended up enjoying pretty much all of them on some level, and the rest is history, pretty much.
Currently my favourite genres are comedy and slice-of-life, though I also enjoy watching more serious shows.