On the show it was referred to as the Death Star, but in reality the one pictured was the Death Star II, both of these sets are very impressive and would be great for any Star Wars fan whether they liked Lego or not!
The Lego Star Wars Death Star II is recommended for ages 16 and up and is an impressive replica built to scale of the original Death Star in the movie. There are 3,417 pieces for you to build and the set also comes with a display stand which indicates to me that it really was just designed to be a display piece.
The Lego Star Wars Death Star #10188 is my preferred set, although that's probably because I'm a sucker for minifigures and this set contains 25 of them! The recommended age for this Lego Star Wars set is 12-20 years and there are 3,803 pieces in the set.
This set looks amazing when completed and allows you to recreate many scenes from the movies - if you decide to frequent any Lego forums you'll find numerous people who will tell you that this is the ultimate set for Lego Star Wars fans.