Kind of getting into this one late, sorry about that.
Rem, if you want to know these things, ask me.
I have always felt that
Kiki's Delivery Service is one of the best starting anime features for general audience viewing. I suppose some few people would be offended by the fact that the main character is a witch, and some may think it is geared towards a younger audience, but for the most part, I believe, everyone will enjoy it. As stated earlier in this thread Ghibli films are great for first viewings, although some of them are a little harder to follow, or show more of the Japanese style of animated fantasy, than others.
Naussica, although a beautiful and enjoyable anime, with a nice environmental message, would not be a good starter anime. In some respects the same is true about
Princess Mononoke. That one is kind of iffy, you will either like it, or you won't. Once you become more familiar with the way Japanese animation is done, I believe it will grow on you. Other Ghibli films that are easy to follow, and enjoy, are
Porcco Rosso,
My Neighbor Totoro,
The Cat Returns,
Spirited Away, and
Howls Moving Castle.
Whispers of the Heart, and
Castle in the Sky I would tend to put lower on the list.
Other works of interest are
Steam Boy, and
Tokyo Godfathers. I believe both of these would have no problem being understood and enjoyed by a new audience. I will state that
Steam Boy gets a bit more far fetched, but it is a non stop action film. I would recommend it over
Akira any day.
For good Sci Fi. Hmmm... I like
Starship Operators. If you want an anime with a feel similar to
Star Trek then that is the series to watch. Another one that has a realistic and believable feel to it is
Planetes, the anime about the "garbage men" of space who are responsible for removing navigational hazards from Earth orbit. For a good space opera I like
Crest of the Stars,
Banner of the Stars, and
Banner of the Stars II, a well thought out galactic conquest anime covering the subjects of genetic manipulation and galactic bigotry. The creator even created his own language for the novels, and they use it in the Anime.
Another fun anime with a sci fi twist is
Unihabited Planet Survive. This is a sort of
Giligans Island style of anime, but not really a comedy. It isn't as dark as
Lord of the Flies, It is closer to
Swiss Family Robinson. I enjoyed watching each of the unique characters grow through the show.
Shows like
Ghost in the Shell are nice, but unfortunately the movie is really hard to follow. The TV series is a lot easier. I wouldn't recommend it to a beginning audience.
For a Fantasy series I would recommend
Seirei no Moribito. It is a beautiful anime, easy to follow, and the whole 8 disk series can be purchased at Walmart for $30.
I also recommend
Nodame Cantabile and it's sequel, a good suggestion.
I can't really think of any other anime about music. Maybe
Piano no Mori It is a great movie, and I think fun for a beginning audience as well.