The Capitol Recordings are a good pick--better recording quality than his earlier Deccas & the performances are more concise than the Pablo Solo Masterpieces. To me, his studio recordings often miss some of the high wire thrills that come across live, but the technical virtuosity is always there.
The first Tatum recordings I really dug into are on 20th Century Piano Genius--they were recorded informally for friends in the '50s. Though clearly not studio quality sound (you can hear people coughing sometimes, or his fingernails on the keys) there's a looseness that consistently draws me in.
Here he is in a great live jam session from the mid '40s--
I haven't given his group masterpiece discs a good listen--will have to do that soon.