Count Basie is my all time favorite swing band leader. He and his linemen were excellent in every respect and they could swing like few others. Personally, I like Basie better than Ellington. Basie's rhythm section is known as the All American Rhythm Section. Their time keeping is discrete and sublime. Basie's trademark is not brilliant virtuosity, though he is by means no slouch on the piano, but first and foremost, a simple spare use of just a few notes to create a catchy, rhythmically intriguing melody that will keep you on your feet and tapping your toes. It's his trademark style
His linemen are equally amazing in their own right. Freddie Green, Lester Young, John Clayton, Jo Jones, and Clark Terry, to just a few of the older and younger mix. Many of them were instrumental in the development of the use of their instruments.
I recommend the Duke Ellington meets Count Basie album.
This cd has these two giants working together and swinging like crazy. You get to hear both bands for the price of one!
No Cootie Williams in the Ellington band at the time being, though. This recording was also historic in a minor way, for those familiar with Ellington's band. Reading the liner notes was great fun!
Also, any recordings with Count Basie and the Kansas City 6 or 7 are awesome. The small group recordings show off much more of their improvisational talents than do the big band recordings. A good high quality cut of Lester Leaps In is an absolute must!
How well known is Count Basie? Well consider him to be among the at least the top 3 best known. Off the top of my head, I would name the Duke, the Count, and Benny Goodman to be the best respected band leaders in swing.