Respect to all anime's but if you watch Bebop you'll experience the wonders of old school anime

Cowboy Bebop and Trigun are also great ones, but I feel that they are better suited for more experienced watchers. A classic anime starter pack should contain this one, I think.

I'm in love with how beautifully Cowboy Bebop is produced. Old western and futuristic space themes mixed with jazz bgm plus interesting anti-hero protagonists, truly a post-modernist gem.
I also really like Yu Yu Hakusho, Slam Dunk, Doraemon and DBZ. Old sports animes in general are one of my favs.

Most western audiences have had an easier time taking to this one apparently due to its western influence, good animation, action, and characters (bonus its a great dub). and honestly if they have trouble with this episodic its going to be tough to suggest most anime which thrives on the art of the episodic tbh

All the above is good.