He was on the scene in New York in the the mid 1930's before hooking up with the Duke Ellington Orchestra shortly after WWII broke out. This was an important time for both Webster and Ellington, so much so that the period became known as The Blanton-Webster Band. (Jimmy Blanton was one of the first jazz bass players to use the instrument for soloing and helped pioneer the "pizzicato" method of plucking the bass strings). Check out one of the most famous tunes to come out of this time, Cotton Tail, where Webster's aggressive growl comes to the fore.
The 50's was a very busy time for Webster as he made a lot of solo albums and found time to collaborate with a lot of great musicians, including Coleman Hawkins, Oscar Peterson and Art Tatum. Here's Time After Time, a song from his 1957 album Ben Webster & Associates. This is a superb example of the sensual tone that he could extract from his tenor sax when it came to playing bluesy ballads.
For me the Ben Webster you want to listen to firmly depends on your mood. His most adventurous work in my opinion was in the early days with Duke Ellington's Orchestra. Ellington knew his musicians very well and composed his music with them specifically in mind. In Webster's later work he appears to be more comfortable with the ballads and in developing his unique sound, rather than challenging himself musically. This is not to take away from any of his later work as some of the albums from the late 50's and mid 60's that I have listened to are superb.