Jazz recommendations for a beginner?

Early jazz: Louis Armstrong,Hot Five/Hot Seven recordings.(The recordings suck,but that's ok;the music does not.)
Swing:Duke Ellington,Live at Newport.
Bop:Charles Parker,Ornithology
Cool:Miles Davis/Gil Evans,Birth of the Cool
Modern:Bill Evans,Sunday Afternoon at the Vanguard.
John Coltrane,My Favorite Things
Giant Steps
These should give you an idea of what kinds of jazz will appeal to you.
Mark C. Gridley's jazz history text is excellent.In it he includes a list of his recommended recordings.
Happy listening

I won't even get into the discussion of what is and isn't Jazz. Simply judging by the fact that you like Krall and Barber and did not care for Miles I would DEFINITELY go for Eva Cassidy as others have recommended. I like Songbird and Imagine and Live at Blues Alley.

Also no one's mentioned Jacintha. Try "Here's to Ben" and "Autumn Leaves"

Barber's "Modern Cool" would also be a good pick.

Holly Cole's fantastic album of Tom Waits tunes titled "Temptation" would be another great choice.

Marco

barber and krall are jazz like john tesh is progessive!

What kind of music do you currently prefer?

Well I didn't mean to insult anybody-if you like Ms Krall then fine,I like lots of things other folks don't.
I tend to think Kind Of Blue( ground breaking as it was in it's day) is on the mainstream of what I would call traditional Jazz.
The other obvious one being Dave Brubecks Take Five-my feeling being that if you don't like these,then well you are into the area of pop/light/smooth or whatever you want to call it Jazz.
Kenny G and the like.
When I started off listening to Jazz,I was recommended Kind Of Blue and well I loved it....that to me is Jazz,the traditional link from what Jazz was into what Jazz became.
A lot of Jazz takes some listening and is challenging and I just think if you don't like KOB well...you are going to struggle with a lot of the greats.
Newbee you are probably right Davis,Coltrane et al they were never mainstream per se but well Kind Of Blue is the biggest selling Jazz album ever...and to me these names along with Ellington and Armstrong are in the line of traditional Jazz.
It's a bit like if you are into movies...Kubrik,Scorsese et al didn't mean ditto at the Box Office.