I agree with the consensus--you can't go wrong with 'Kind of Blue' as your first draft choice. And you can't go wrong watching Ken Burns's excellent series. On top of that, the accompanying CDs are not only relatively cheap, but wonderful introductions to the legends. Buy as many of them as possible (I believe there are 24). After that, you might consider box sets, which have been a godsend to jazz lovers like me who do not already have comprehensive collections--the Monk Riversides, the Armstrong Hot Fives & Sevens, the Ellington Centennial collection, the Holiday Columbias and Verves, Coltrane's classic quartet and his Village Vanguard Sessions, the Rollins' RCAs, Miles at the Plugged Nickel ...the list goes on and on. Although few of these boxes are cheap, if you are patient you can eventually find good deals on them in the used market. I think of those listed above, I paid full price only on the Billie Holiday Columbia recordings, because I just could not wait to hear them remastered. What a revelation!
In any event, you'll get some good advice from the fine folks on this site. I'm a relative newcomer myself, and I've benefitted greatly from the expertise and insights of A'Goners.
Oh yeah, after you get 'Kind of Blue', don't wait long to pick up Charlie Parker's 'The Legendary Dial Masters,' a double CD set. These recordings must be included in any list of essential jazz. If you want to try somebody new, look up James Carter--he's the real deal.
Have a great time!