Right, I should have been a little more exact about the language used for tragedy -- it's mostly Attic, but there's a fair amount of Epic and Doric mixed in, and a certain amount of vocabulary that's different than Attic (I know this because when I did prose comp in Germany the professor kept marking my word choice as "poetic")
William Annis has a good article on the topic: http://www.aoidoi.org/articles/dialects.html
Like I said above, the transition from one dialect to another isn't so difficult. If you've learned Attic, you can read Homer, or tragedy or lyric poetry or whatever, although it wouldn't hurt to look over some of the forms that are different in Homer (pronouns are a bit different, for example).
My university often has second-year Greek courses reading Homer -- in spite of the differences from Attic, Homer is simpler than many Attic authors for beginning students in a number of ways: there's a lot of formulaic phrases, and his syntax is pretty straightforward, which tends to be a huge challenge when reading prose.