Some good starting points would be...
Gunbuster and Diebuster, as well as Gurren Lagann for epic mecha action.
Soul Eater, ease you into shonen (where nearly all of us started) without being shitty.
Anime to someone who's never watched it before can be very, very odd. I'd suggest Potemayo right off the bat to get all the "what the hell am I watching?" out of you quickly.
Also, the Japanese style of humor takes some getting used to. I'll let someone else suggest some comedy, as I don't know any that doesn't depend on a massive amount of references.