I don't know that there is any set order that you need to watch the Batman cartoons in, but I can tell you that there are a number of Batman cartoons that have been made.
I would suggest checking Wikipedia's page here which has a great listing of Batman's live action and animated appearances through the years- http://en.wikipedia.org/wiki/Batman_franchise_media
I am a big fan of both DC Comics and Marvel Comics and I enjoy watching most all the various live action movies and TV shows and cartoons based on them. For the most current Batman show, you can check out "Beware The Batman", starting on Cartoon Network on July 13th.
"I am the Way, the Truth, and the Life. No man comes to the Father but by me." - Jesus (John 14:6)
"You can do anything you want to do if you put your mind to it."- MacGyver