speaking as an anime outsider, I have watched, or atleast tried to watch, quite a few anime. I say, the less tropes the better. Anything with school girls is a no, anything that occasionally goes into...super-deformed mode, I think? Not sure what you call it, but it seems to be used for occasional "comedy" scenes. That's also out, because that shit is just weird, and Japanese humor really isn't that funny to outsiders. Most of it seems to be based around either Japanese culture or awkward slapstick. Hell, I had to do a few google searches to find out that a nose-bleed is a symbol for being aroused. Shit is weird. Also, something with a simple title is good. Japanese words, and some names, are just difficult to say/read to non-Japanese versed folk.
So yea, Cowboy Bebop. That being said, don't expect it to suddenly make them want to watch other anime. It was an excellent show, but it is also the least anime-like anime there is, which is why it's so appealing to outsiders. After watching that, I watched FMA (the original!) and Death Note. They were both good, but they still had some damn annoying things about them. And don't even get me started and FMA: Brotherhood...
Again, this is all from an anime outsiders point of view. I figured my input would be helpful, since I'm really part of the group you seem to be trying to appeal to. Most importantly, do not try to force it on people. Anime is not for everybody, and having people keep telling you "Oh, you just need to watch THIS one! And then THIS one!" is just really fucking annoying, and is a fantastic way to forever turn them off the medium. If they ask for recommendations, go for it, but don't start bothering people about it.