Like many people have said, the Miyazaki movies is probably the best place to start. Rurouni kenshin and Full Metal Alchemist are also really great places to start. If you get past those, Code Geass is pretty great. So is Persona 4 the Animation. Subs generally tend to be better, but they can be pretty intense when you're just jumping in. A number of the Miyazaki movies have great dubs, especially Howl's Moving Castle, and Code Geass also has a pretty great Dub. Everyone's experience is different, but for someone who doesn't speak Japanese, starting with dubs helped me get into Anime.
I wouldn't want Brad to go anywhere, even if sleepy brad is sleepy (probably just producing content for the sleepy brad tumblr). That being said, I would love if they added Rorie to the podcast crew, he has a lot of random tangents to add, and those are the best parts of the bombcast, when they get lost on weird tagents.