There is something for everyone!
Manga is categorized by audience first, then by genre. Primarily, there are 5 main types of Manga:
Shonen: Manga aimed at tween and teen boys
Common themes are action, adventure, friendship, coming of age.
Shojo: Manga aimed at tween and teen girls 
Common themes are romance, drama, coming of age.
Seinen: Manga aimed at men 18 and older
Common themes are action, violence, adult themes.
Josei: Manga aimed at adult women
Common themes are romance, drama, adult themes.
Kodumomuke: Manga aimed at young children
These series will often be cutesy, moralistic, and fun. Both the Pokemon manga and anime are probably the most well-known examples of a Kodomomuke series.