Tengenn Toppa Gurren LagannDP155ToneZone said:-snip-
Though not really. That one, while an incredibly good anime, is about as far from Western tastes as one can get (as a sample, by the end of the series, people are throwing galaxies at each other as weapons). I'd recommend watching it eventually, but not as a starter. It's just likely to get way too zany for your tastes.
Good entry animes are: Trigun, Ghost in the Shell and Outlaw Star.
Trigun is basically a Western, and the main character, Vash the Stampede, is amazing. It's my favorite anime of all time.
Ghost in the Shell is about a special counter-terrorist task force in cyberpunk Japan. I enjoy it, and it's not too much of a departure from some common themes in Western media.
Outlaw Star is a rather interesting bit on pirating/treasure-hunting with spaceships. Definitely one of my favorites.