Anime is a type of animation that started in Japan. Basically, you can call it a Japanese version of cartoons. However, anime has some big differences. Where American animation tends to be geared primarily towards children, there are actually many types of anime, geared for many ages and interests. There are many different thematic styles of anime, including those centered around robots, romantic anime, fighting anime and so on.
Manga is simply the Japanese version of comic books or graphic novels. Many anime series are based on a manga series. Any anime fan would love the original manga their favorite anime is based on. For original Japanese manga, you can usually find some on eBay and at Japanese importers like JustManga and Manga.com. For the most popular anime series, like Inuyasha, you can find English translated manga books at many major bookstores.
Some anime and manga series have a live action version, like Sailor Moon, that a Sailor Moon fan would likely be interested in. There are many Japanese drama series aimed at tweens and teens that usually take place in school or high school. Check out Nodame Cantabile, Hana Yori Dango and Gokusen, each was based on anime or manga series or both. Look for these series at places like PlayTech-Asia and on eBay. Make sure to get the English subtitled versions.