Dragon Ball tells of the story of Son Goku (for any of you who know of the Chinese tale 'Journey to the West', you probably recognise this name as well as the plot) and his quest to find the mystic Dragon Balls. These, when gathered together, summon the great Shenlong who will grant any wish asked. Along the way, meet the Turtle Hermit, who teaches Goku the basics of martial arts, Bulma, Krillin, Chi Chi, Yumcha and a whole host of other colourful, wonderful and exciting characters.
Dragon Ball Z continues from where Dragon Ball finishes. The Earth is at peace, Goku is considered the strongest martial artist in the world and has now had a child with his wife, Chi Chi. This story introduces the famous Super Saiyan, exposes Goku's past along with other characters, and goes just a little silly (The Earth is destroyed nearly twice over). Read along as Goku battles against his own limits, befriends enemies and continues to save humanity time and time again.
These two stories are vastly different from each other. Dragon Ball is silly, a little immature (perfect for boys aged 12) and a nice introduction into the world of manga. Dragon Ball Z sets the stage for a lot of manga to follow on afterwards. It introduces power levels, transformation to achieve stronger states and big, epic battles showing martial art prowess. These three things are typical in your standard action-packed manga usually for those aged 13 to 17. Both of these have been series I have thoroughly enjoyed and introduced me to so many different series and continued my enjoyment of manga. A good, fun read for everyone who enjoys all things action.