This is where it gets interesting! The Clone Wars (Movie first, then TV show). Cartoon Network started this series and it had a little bumpy start, but season after season this show got better and better. The TV show took place in the years between the second and third prequel movies.
Up to season 5 the show was an amazing tale of the path of the Star Wars universe. Season 5 was somewhat disappointing at first when Cartoon Network tried to make the show more appealing to children. During this time, it lost much of its fan-base of hardcore Star Wars fans. It tried to save itself, but failed and was cancelled before Season 6 could be released.
Luckily Netflix picked up the show for a final season (that was already produced, however not released). If I could suggest any Star Wars show to watch, it would be this one. This show is currently still on Netflix and worth the many hours it takes to watch the complete series.